# Acoustic Shell Optimization in Opera Houses for Concert Halls
## 3 The Case Study
### Acoustic Modelling, Measurements and Calibration  
The construction of the 3D model is a very long time-consuming process that requires the creation of a continuous closed surface volume that satisfies the requirements imposed by the acoustic simulation software (ODEON) and the necessary geometrical simplifications (Figure 6). The geometry reduction in room acoustics modelling is a complex topic, with regards to controlling sensitivity and the modelling uncertainty, which would require a separate work on its own to explain in detail [44; 45]. For this case study, some absorption \begin{table}
\begin{tabular}{c c} \hline Volume V & 18,200 m\({}^{2}\) \\ Area of the floor occupied by audience chairs Sa & 816 m\({}^{2}\) \\ Acoustic audience area SA & 1227.6 m\({}^{2}\) \\ Stage area So & 600 m\({}^{2}\) \\ Area of the proscenium curtain Sp & 277.75m\({}^{2}\) \\ Acoustical absorption area ST & 1525.4 m\({}^{2}\) (excluding the pelmet) \\ Number of seats in hall N & 1633 \\ Average room height H & 26 m \\ \hline \end{tabular}
\end{table} 
Table 9: “Opera di Roma” data. coefficients were chosen from the literature, and some were found through measurements, as better explained in the paragraphs below. The scattering values were chosen based on recommendations given by the ODEON programme [46]. The SketchUp 3D modelling software was used first, to create a virtual geometric model. The model was exported to Odeon, to carry out the acoustic assessment; absorption coefficients, source, and receivers' positions were specified (Figure 7). The length of the room's impulse was set manually considering the measured data to calibrate the model. The absorption coefficients of all materials were defined first according to the reference values in the literature. The creation of the virtual model was preceded by some preliminary considerations about the theatre volume: some authors [47] propose that the volume which must be taken into account is that of the main hall, excluding the volumes of the fly tower, the boxes, and the gallery. In the end, the proposal by [PERSON] and [PERSON] [38], accepted by other researchers [28] was followed. It argues that opera houses can be analyzed as coupled volumes if they have large stage houses or hard reflecting surfaces characterized by partial draperies or empty stages; otherwise, only a single volume must be considered. Figure 6: Acoustic model with sound waves representation (Odeon). Figure 7: Source (red) and receivers (blue) positions in plan (**a**) and in section (**b**). As the way sound energy propagates between the hall volume and the fly tower is still a subject of research [42], a decision was made to consider the virtual model as one single volume and to avoid modelling the fly tower. The measurement survey aimed to check the reverberation time T30 and C80, considering those to be sufficient for the calibration process [48]. The measurement procedure was in accordance with ISO 3382-1 [28]. The sound was given by an omnidirectional source: a dodecahedron speaker with a sine sweep signal. Free-field microphones in class 1 (BSWA TECH MPA201) were used. They were wire connected to an Integrating Sound Level Meter and Real Time 4 channel analyzer (Soundbook), and they were placed faced up, in every chosen receiver position, to capture the diffuse sound field. The signal analysis was developed using Samurai software. Measurements were repeated twice in every receiver position. During the measurements, with it not being possible to set an acoustic shell on stage, it was decided to configure the hall with a closed house curtain, while the source was placed 15 cm from the stage front, at a 1 m distance from the longitudinal axis of the hall. Temperature and relative humidity parameters were equal to the ones in the simulations. The hall was unoccupied. The chosen configuration for the measurements was considered to minimize the modelling uncertainty for different reasons.