Null angles and vertical control
However, extrapolating from the AES graphic, though It seems counterintuitive, increasing the center to center spacing narrows the arc between nulls (given the same crossover point.) I hope I’ve determined that correctly.
That's right, the further apart the drivers are placed, the narrower the arc between nulls.
I was wondering if you think basic RTA capability could be used to determine vertical off axis response nulls? For example, after using the Altec method to determine correct horn fore/aft alignment, could I move my mic up or down to the assumed null point and check for a notch or actually a falloff at the crossover frequency? If this is visible and reliable, driver center to center spacing could be fine tuned in this manner, checking for symmetry both above and below at null axis positions.
If you're using non-gated measurements, it's best to look for null angles outdoors. Lay the speaker on its back and use a boom or something (acoustically small) to get the microhone over the speaker a few feet. You'll be able to see the reduction in amplitude caused by the nulls.
If you have equipment that allows you to setup gating, you can do pseudo-anechoic measurements indoors. This won't let you see the bass, but you can see what's happening in the crossover region with a gated measurement.
But if you're measuring with an RTA, do it outdoors so you won't see notches from boundary reflections.
For all these measurements I assume the microphone should reference the center point between the two drivers, not the horn center, as the axis of measurement.
If you position the microphone on-axis with the horn, it is closer to the horn than the midwoofer. The midwoofer is off-axis at an angle but the tweeter is not.
Best to position the microphone far enough away that both woofer and tweeter are as close to being on-axis as possible. The trade-off is the further away you get, the more noise you have to overcome by driving the speaker louder.
For a speaker like this, I'd say two meters is a minimum.
Another assumption I hold: As the listener moves away from the centerline of maximum phase reinforcement vertically between drivers, phase cancellation increases progressively to a maximum at the null. Beyond that, reinforcement may begin if the null has not been properly aligned with the end of the dispersion pattern at crossover frequency. So it’s important to know what the dispersion really is at crossover, and have a midwoofer which is very close in this characteristic.
On-axis, the sound sources are coherent and completely in-phase.
As you move off-axis in the horizontal plane, the same thing holds true. The only thing that changes response through horizontal movement is the directivity of the sound sources. Since they're matched through the crossover range, what you see is nearly omnidirectional radiation gradually narrows to 90 degrees, where it stays fixed by the horn up through the rest of the band, or at least to the point where the exit angle of the compression driver begins to set the pattern. In the top octave, the throat features set the pattern.
As you move off-axis vertically, phase between woofer and tweeter begins to change. Summing remains coherent until the phase change exceeds 90 degrees, where it begins to transition to destructive interference. This happens at around 1/2 the null angle.
As you get close to the null angle, the phase between woofer and tweeter becomes nearer to 180 degrees. This causes reduction in amplitude in the crossover overlap band at the null angle. As you move further off-axis the amplitude will rise again if the HF horn has angular coverage past the null angle. Likewise, above the crossover point, there are no nulls because the woofer is not making sound to interfere with the tweeter. So above the crossover point, the horn sets the radiating angle. Here again, if the horn provides a vertical pattern that is taller than the null angle, then the pattern will dip at crossover and rise again at higher frequencies.
If the null angle is small and the tweeter is too small to provide vertical control at that frequency, then what you'll see is the vertical pattern narrows at crossover because of the nulls and widens above it because the horn is too small to provide much control. As the horn gains pattern control the coverage angle will narrow again.
If the null angle is wide, the tweeter's pattern is narrow and the horn is large enough to provide control, what you'll see is narrowing in the crossover band both because of the horn's pattern control and because the summing between sound sources is transitioning from coherency to destructive interference. You will not distinctly see the nulls because they are effectively outside the pattern of the horn. They will appear as a small dip on the polars, outside the coverage angle.
If the null angle is slightly greater or approximately equal to the horn's vertical coverage angle, and the horn is able to control the pattern down to nearly the crossover point, then the nulls serve to punctuate the pattern. The nulls will not be as pronounced as they would be using a horn with taller vertical pattern. You will see the null dip, but above it there will be less energy, so the dip will be less pronounced.
The taller the vertical pattern is beyond the null angle - either by design or by ineffectiveness of pattern control - the more pronounced the off-axis nulls become.
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