Overhead
canopy arrays are used in auditoriums to blend the direct and early
reflected sound, increasing speech intelligibility and enhancing
musical clarity and intimacy. Traditionally, non-optimized, periodic
flat panels or arcs have been used and their placement has been
either aesthetic or based on geometrical optics. If not properly
designed, tilted and arrayed, a canopy can provide uneven coverage,
typically exemplified in minima and maxima in the sound pressure
level. In addition, these simple shapes can be diaphragmatic, leading
to a loss in low frequency sound. To solve this problem, RPG developed
a powerful shape optimization software, which optimizes the shape,
tilt and arraying of the canopy array and eliminates all of the
guesswork. The Waveform Spline is an optimized one dimensional wavy
panel that provides uniform coverage over the entire stage or audience
area. Novel Class A fire safe honeycomb GRG laminations also minimize
diaphragmatic absorption.
Problem
Flat panel arrays provide uneven sound pressure levels over
the audience area. Listeners experience sound level minima when
the geometrical reflection point for a receiver is between panels
and maxima when the geometric reflection point lies on the panels.
Coverage can be improved by curving or shaping the panels, but there
is no guarantee that optimum results will be obtained and consequently
uneven response is often experienced.
Solution
To solve this problem, RPG developed the first Shape Optimization
program, which automatically determines the best shape, tilt and
arraying to insure uniform coverage. The Shape Optimizer combines
the power of the boundary element and multi-dimensional optimization
techniques, incorporating the diffusion coefficient as the metric
of optimal performance. The Waveform Spline provides optimal ensemble
for musicians on stage and uniform coverage in the audience. Each
canopy element has the same optimal shape for aesthetic reasons,
but independent tilt, insuring uniform coverage by the forestage
canopy in a definable number of rows in the front of the audience.
Diffusion
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Figure
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Shape
Optimizer
In Fig. 1, we show the canopy section, sources/receivers on stage
and receivers in the audience. In Fig. 2, we show the sound pressure
level (SPL) at musician’s ear level over the entire stage
from a source in the middle of the stage. The canopy is flat and
extends across the entire width of the stage with gaps as shown
in Fig. 1. Note the level is constant across the stage, but there
are severe dips and peaks front to back. The Shape Optimizer examines
thousands of potential canopy shapes in an attempt to provide the
flattest coverage possible, based on the size and shape constraints
imposed. Fig. 3 shows the dramatic improvement over the flat panel
canopy. The standard deviation from uniformity (0 dB is uniform
coverage) is plotted in Fig. 4 for the flat panel, a 5’ and
10’ radius traditional arc , an angled panel and the optimized
Waveform Spline. The improvement is dramatic.
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