Stage Canopy Optimization - Part I

Fig 1. Location of stage canopy elements on a large convex arc above the stage.

We begin a two part presentation on a new approach to design and evaluate stage canopies. This case study is a result of our CHAOS™ interaction with a leading acoustical consulting firm. The boundary element method offers acousticians the most accurate way to predict and evaluate the performance of a stage canopy. RPG has combined this approach with a search engine to also determine the optimum surface shape. We will describe the optimization of a stage canopy, illustrated in Fig. 1. It consists of an array of similar elements lying on the arc of a large circle whose radius is variable. The elements extend across the full width of the stage and are spaced for lighting or to access the volume above the canopy. To illustrate the improvement optimization affords, we will compare the optimized “S” shape, with traditional arcs of 5’ and 10’ radius of curvature, a wedge or elbow shape, and a flat panel shown in Fig. 2.

Fig 2. Illustration of the various canopy element shapes evaluated in the optimization.

Optimization Parameters
To evaluate the effectiveness of the thousands of surface shapes considered in the iterative optimization, we have defined a cost parameter, which is the average standard deviation (referred to as Diffusion) in dB of the scattered pressure at the receivers, from all of the sources on stage. It is evaluated at 1/3-octave center frequencies over the desired bandwidth.

Results
In Fig. 3, we show the scattered pressure using flat canopy elements from a source in the center of the stage at 2 kHz. Notice the specular hump in the center of the stage and how irregular the coverage is from the front to the rear of the stage. The ideal coverage plot would be essentially flat with a low standard deviation. To find an optimum curved shape, the curve optimizer program searches for the best combination of a specified number of harmonic sinusoids (e.g. 4). The result is the “S” shaped profile in Fig. 2. The more uniform coverage offered by this shape is shown in Fig. 4. In Fig. 5, we compare the average standard deviation from all of the sources, to all of the receivers, for all of the canopy shapes examined, as a function of frequency. It can be seen that the optimized canopy offers a lower standard deviation than any of the conventional shapes. In Vol. 3, Issue 4, we will discuss an approach to optimally distribute the energy created on stage, between stage and audience.

Fig 3. 2 kHz scattered pressure from flat canopy elements at all receiver locations. The source is located in the center of the stage.

Fig 4. 2 kHz scattered pressure from optimized canopy elements at all receiver locations. The source is in the center of the stage.

Fig 5. Comparison of the average standard deviation (Diffusion, dB) as a function of frequency for all of the shapes examined.