RPG Waveform Spline G

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 - click to enlarge

Figure 1	Figure 2
Figure 3	Figure 4

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.

Seamless Spline Arc

Installation
Installation is simple using integral metal hair pin connectors . Simply attach suitable airline cable for dead hung installation. Spline panels can be seamlessly joined end to end forming an extended arc. 

Applications
Starpoint High School, Kresge Auditorium 


Specifications
Product Option Sheet
Waveform® Spline panels are available in 4’x8’x9” and 4’x12’x12”. Three surface weight options are available 3 lb/sf ¼” GRG, 4 lb/sf 1 5/8” GRG/Honeycomb/GRG (GHG), and 5 lb/sf GHG.
Panels can be factory or field painted. When joined into aperiodic arrays and extended side to side, seams can be filled and sanded and field painted.

Features
Optimized shape
Optimized arraying and positioning
Integrated mounting hardware
Seamless Tiling in both directions
Glass Reinforced Gypsum (GRG) meets Class A fire safety codes
GRG or GRG/Honeycomb/GRG (GHG) composite
Field finished

Benefits
Optimized shape insures uniform coverage
RPG provides optimal arraying and tilting to insure uniform coverage and eliminate guess work in the field
Adjacent panels seamlessly tile for wide area coverage simulating a single canopy element
Spline panels and be used independently or tile side to side and front to back for wide area application
GRG is non-combustible and hence can be used in all applications requiring a Class A rated material
In addition to 1/8”, 1/4” thickness GRG, RPG also offers a novel GHG composite 1 5/8” thick for improved damping and stiffness
Field finishing allows joints to be taped forming a continuous surface, which can also be field painted
Installation is quick and easy using integral metal hairpin hanging loops and aircraft cables.