# Simplified Fly Tower Modeling for Preliminary Acoustic Predictions in Opera Houses
## 3 The Case Study
### The Acoustic Model  
The 3D model construction is a very long time-consuming process because a continuous closed surface volume must be created that satisfies both the requirements imposed by the acoustic simulation software (ODEON 12) and the geometrical simplifications (Figure 9). This is a complex topic in room acoustics, which requires separate work on its own [35; 51].  
For the case study, most absorption coefficient inputs were chosen from the literature, and some were found through measurements. The scattering values were defined based on recommendations given in the literature [36; 52] and the ODEON manual [53].  
The SketchUp 3D software version 18 was used first, to create a geometric virtual model. The model was exported to the acoustic software, to carry out the acoustic assessment; absorption coefficients, source, and receivers' positions were given (Figure 10).  
The length of the room's impulse was set manually starting from the measured data to calibrate the model.  
Figure 10: Sources (red) and receivers (blue) positions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Absorption Coefficients**} \\ \hline Hz & 125 & 250 & 500 & 1000 & 2000 & 4000 \\ Heavy velvet & 0.32 & 0.65 & 0.75 & 0.85 & 0.9 & 0.9 \\ Rigid columns & 0.18 & 0.15 & 0.11 & 0.88 & 0.07 & 0.05 \\ Wooden Floor on joists & 0.15 & 0.11 & 0.10 & 0.07 & 0.06 & 0.07 \\ Carpet on concrete & 0.15 & 0.12 & 0.12 & 0.07 & 0.06 & 0.07 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Absorption coefficients [40].  
Figure 9: Acoustic model of the hall.  
Before creating the virtual model, some preliminary considerations about the theater volume were analyzed. Some authors [54], in fact, propose the main hall as the volume which must be taken into account, excluding the volumes of the fly tower, the boxes, and the gallery. In the end, the proposal by [PERSON] and [PERSON] [55] was followed, for which opera houses can be analyzed as coupled volumes if they have large stage houses or hard reflecting surfaces; otherwise, only a single volume must be considered.  
The measurement survey aimed to check the Reverberation Time T30 and C80, the two acoustic parameters considered sufficient for the calibration process [56]. The measurement survey was in accordance with ISO 3382-1 [17]. The sound came from an omnidirectional source: a dodecahedron speaker with a sine sweep signal. Free-field microphones in class 1 were used.  
The measurement configuration was that of the hall with closed fire curtains, with the source placed 15 cm from the stage front, at a 1 m distance from the longitudinal axis of the hall. The hall was unoccupied, and the temperature and relative humidity parameters were equal to those in the simulations.  
In the calibration process, the uncertainty in fly tower modeling was avoided by replacing it with the fire curtain.  
The hall absorption coefficients needed to be identified. The calibration process was started considering the seating area as the main absorption surface of the hall, and using 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] [57,58]. Absorption coefficients of the seating area were referred to the medium upholstered seats [40].  
The measured RT and C80 values for the calibration process referred to the theater configuration in which the fire curtains are closed. The difference between the simulated and the measured values is within one Just Noticeable Difference JND [17] (Figure 11).  
After the calibration, the fly tower volume was added to the simulation model, and the source was moved 1.7 m away from the proscenium, inside the stage.