Oblate Spheroid Waveguide - Consolidated Construction Thread

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From my data, the ideal would be an 18" waveguide with a 12" woofer. This would elliminate all the flaws that I see in practice. But such a combination would not be an attactive speaker for a lot of reasons. the next best, and what I would build for myself, is a 12" woofer and a 15" waveguide. Simulations indicate this combination to be a very good match.

Please help me understand the above quote from @gedlee
 
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