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RE: that may well be the case, Dave ...

Did you look at Figure 2 (and the others for straight line sources) in the Ureda paper?
It's well described in Section 3 of his paper.

The math does get a little involved, but the simplified function is noted in 3.3.

Implementation of the crossover is key in real-world systems, and much depends upon the frequency range the line source is driven. I suspect that's what you're noting with your "no vertical component" observation.

I hope you're not arguing that line-sources have no inherent disadvantages relative to "conventional" and/or point-source radiators. All of them have inherent advantages and disadvantages. If you add up all the pluses and minuses, a point-source radiation characteristic would be optimum in a free-field environment. But those are (essentially) impossible to construct. (At least for a full range speaker system.)

The objective in any speaker system should be to make them as small (acoustically) as possible. Any time you make them larger, things get more complicated. :)

Dave.



Edits: 08/15/15

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