I didn't find any polars of the 90x50 horn by itself, but I did look at the polars of the loudspeakers that use it. From those charts, it looks to me like the directivity of the horn is a lot like the H290 I use. Aside from the nulls, it seems to start having vertical control around 3kHz.
Notice that the higher the crossover, the narrower the null angles are. Ones crossed over high have closely spaced nulls. Crossover lower and the null angle widens.
Also pay attention to the size and shape of the notch. It's narrow and deep, as much as 10dB and sometimes a bit more right at the frequency and angle where path length difference is exactly 1/2 wavelength, corresponding to 180 degrees phase difference. Then there is a wider region where the difference represents a phase anywhere from about 150 to 210 degrees or so. This is partial cancellation and it happens over a wider frequency range. That doesn't show as well in the JBL charts because the resolution isn't real high, but you can still see it.
Look at the speaker with the axisymmetrical horn. See how vertical off-axis output reaches the zero reference level both below crossover and also above it? Above about 3kHz, you have full output at all angles in the coverage pattern. Below about 1kHz, you also have full output. The nulls appear in the 1.5 to 2 octaves in between, marked with a 5dB to 10dB valley (or valleys) in that region. So off axis what you hear is full treble but a huge suck out in the overtone region from 1kHz-3kHz. Plenty of top-octave splash for the ceiling and floor.
Now look at the asymmetrical horn. At low frequency below crossover, you have full output. But at high frequency, the vertical pattern is more narrow. This reduces output at large vertical angles from -5dB to -10dB or more, depending on the angle. Since it's a 90x50 horn, you should expect -6dB at about 25 degrees up and 25 degrees down, and even less output at larger vertical angles.
At the null angles, there is a pretty well defined notch. In some of the JBL models, I think I would have been more careful to place the notches further outside the horn's vertical pattern; In some cases, they have nulls at 10 degrees. But it still shows how this works. Those notches can be used to punctuate the edge of pattern control. Above the crossover range, the horn does the work. If the horn is large enough, it can limit vertical off-axis output at or near the crossover point. If not, the pattern will widen briefly above the crossover point and then settle back down to a narrow angle just above that, where the horn is able to provide directional control.
If we place that null notch just outside the pattern, and if the horn has directional control down to the crossover frequency, you'll have a straight line of vertical coverage. Usually this ideal isn't realized, and you have about an octave above the crossover where output is higher at the edge, followed by the horn gaining control and bringing the output back down again up through the rest of the audio band. But except for the bump between 2kHz and 3kHz, output is fairly flat from the crossover point up.
Have any of you tried using the
four Pi crossover? You might try breadboarding one and trying it on your speakers. I think it will work very nicely with a speaker having the horn and woofer flush mounted on the baffle. From what I can tell from the photos posted here, I think you should get pretty similar response to the four Pi with it.
I use the Eminence PSD2002 and B&C DE250 drivers. The B&C DE250 is a little bit higher sensitivity, so R1 and R2 changes are needed. It's easy to set the crossover for use with just about any compression driver by changing those two resistor values. I've worked out a
chart that helps select the right values.