Figure 1 shows the canopy design for a new recital hall containing an array of twenty 6' x 14' sinusoidal shapes at various heights, forming an interesting elliptical bell-shaped pattern that covers both the stage and audience. As part of RPG®’s CHAOS™ program, we collaborated with the architect and acoustical consultant to optimize both the shape and tilt of each element, while maintaining the motif desired by the architect and client.

Optimization Parameters
In this example, the goal of the optimization was to achieve uniform coverage at all receiver positions from all sources over a frequency range of 100- 3,000 Hz. The maximum allowable depth was 2'. The Shape Optimizer™ was used to determine the shape and also the tilt of the canopy elements with respect to the horizontal plane. Figure 2 illustrates the optimized shape and tilt of four of the twenty optimized canopy elements, the 10 source positions (solid diamonds) on stage, and the 50 receiver positions (open squares) in the audience and on stage. The sources and receivers on stage represent the musician’s instruments and their ears, respectively.

Figure 1. Reflected ceiling plan showing the 20 canopy elements. Four canopy elements, shown in black, are illustrated in section.

Figure 2. Four of the twenty canopy elements, the 10 sources lying on stage (black diamonds), and the 50 receivers (open squares) in both the audience and on stage are shown.

Results
Notice that the stage canopy elements have less tilt to provide ensemble reflections to the musicians on stage as well as the fore-stage area. The rear canopy elements are tilted at a greater angle so that sound projected from the stage is scattered into the audience area.

Acousticians have used performance specifications to indicate desired objective parameters, such as reverberation time, based on the number of Sabines of absorption. The Shape Optimizer™ now makes it possible to quantify the degree of scattering as well, so that performance specifications can also contain diffusion criteria. This is a significant development for architectural acoustics and provides another step forward in predicting the performance of virtual spaces.

The performance of the canopy can be quantified by the random incidence diffusion parameter in dB. This parameter is determined by the average standard deviation of the 1/3-octave sound pressure level at all receiver positions from all sources over the frequency bandwidth of interest. Figure 3 compares the optimized performance with that of a flat canopy panel (Zero standard deviation indicates the desired scattering coverage has been fully realized). The degree of scattering can be specified. In this example, uniform scattering was specified. Figure 3 illustrates how the random incidence diffusion parameter has been lowered significantly over the frequency band of interest, compared to a flat panel.

Figure 3. The random incidence diffusion parameter in dB for the optimized canopy is compared with a flat canopy.

The Shape Optimizer™ produces a DXF file, which is used to create templates for either wood bending or fiber-reinforced gypsum fabrication. The CHAOS™ program allows RPG® to work with the design team by offering optimization only, materials only, or a fully rigged and installed canopy and acoustical shell system.

Home: Research & Development: Research Topics: Stage Canopy Optimization - Part III