Circular-arc loudspeaker line arrays composed of multiple loudspeaker sources are used very frequently in loudspeaker applications to provide uniform vertical coverage [1, 2, and 4]. To simplify these arrays, the arrays may be formed using multiple straight-line segments or individual straight-line arrays. This approximation has errors because some of the speakers are now no longer located on the circular arc and exhibit a “bulge error.” This error decreases as the number of segments increase or the splay angle of an individual straight segment is decreased. The question is: How small does the segment splay angle have to be so that the overall performance is not compromised compared to the non-segmented version of the array? Based on two simple spacing limitations that govern the upper operating frequency for each type of array, this paper shows that the bulge deviation should be no more than about one-fourth the center-to-center spacing of the sources located on each straight segment and that surprisingly, the maximum splay angle and array radius depends only on the number (N) of equally-spaced sources that are on a straight segment. As the number of sources on a segment increases, the maximum segment splay angle decreases and the required minimum array radius of curvature increases. Design guidelines are presented that allow the segmented array to have nearly the same performance as the accurate circular arc array.
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