In Part 1 we compared conventional geometrical canopy shapes with an optimized curved surface. We showed how optimization can be used to design better stage canopies and compare several potential options for a particular project. The results indicated that optimized shapes can offer an improved performance over conventional periodic arcs, wedges and flat panels. In this second installment we show how optimization can also be used to control the ratio of scattered energy between the stage and the front section of the audience.

The canopy in Figure 1 consists of an array of similar, spaced, optimized shape elements. Each canopy element can be individually tilted for optimum coverage on stage and to produce the desired distribution of stage-generated energy between stage and audience. The canopy elements extend across the full width of the stage and are spaced for lighting or to access the volume above the canopy.

Fig 1. Configuration of shaped and tilted stage canopy elements.

Optimization Parameters
In this optimization we specified that the scattered energy should be as uniform as possible on stage (-9 - 0 m) and in the audience area between 4 and 10 m from the edge of the stage. In addition, we searched for the best shape and orientation to reduce the level in the audience by 3 dB of what it is on stage. To accomplish this, the Shape Optimizer™ varies the shape and tilt of the 5 individual canopy elements. At each iteration of the optimization, the standard deviation of the scattered pressure, indicated in Figure 2 for a source at the rear of the stage and at 1 KHz, is monitored as an indicator of performance. The Shape Optimizer™ cycles until it finds the best shape and tilts that yield the lowest standard deviation in the specified bandwidth (i.e. 100 to 3,000 Hz) at all observer positions, from all source positions.

Fig 2. Comparison of the sound pressure level on stage and in the audience at 1 kHz, for a source at the rear of the stage, for a flat and optimized canopy.

Results
In Figure 2 we show the scattered sound pressure at 1 kHz from a flat canopy (thin line) versus an optimized canopy (thick line-circle). The flat canopy exhibits significant fluctuations both on stage and in the audience area of interest. The optimized canopy, on the other hand, displays a more uniform response. Since we need to evaluate the uniformity of the scattered pressure at 1/3-octave intervals over the bandwidth of interest at all receivers from all sources, we must find a way to condense this information. The diffusion spectrum accomplishes this in graphic form. The diffusion coefficient in dB at each 1/3-octave frequency band is the average standard deviation of the scattered sound pressure level at all of the receivers from all sources. A value of zero represents uniform scattering with zero deviations from the mean. Fig. 3 illustrates how the optimized canopy displays significantly better performance than the flat panel over the bandwidth of interest.

Fig 3. Comparison between the diffusion coefficient of a flat versus an optimized canopy.

In conclusion, we have tried to show that the Shape Optimizer™ can provide consultants with a powerful new AcousticTool® to design optimum surface shapes, which comply with architectural motif and dimensional constraints, while providing the desired scattering coverage. Once the shape is optimized, it can be incorporated into RayNoise® (a powerful geometrical room simulation/auralization program from LMS that RPG is distributing) to allow auralization of the shape in the room, before it is built. RPG’s expanded woodworking or fiber-reinforced gypsum manufacturing capability and painting facility, can make the design a reality.

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