I'm learning as I go here too, but I think I can help you with a couple points from this last post.
The beamwidth does vary - but that's not really relevant to the issue of lobing at the crossover and the ceiling reflection. With the two-way SEOS designs, there will be two patterns of beamwidth variation. The woofer will transition from omni-directional radiation to narrow beaming. This is simply a function of the relationship between driver size and wavelength of sound. It's the same in the vertical as horizontal. It can be influenced by baffle size and shape to some extent (this is part of the purpose of baffle walls). In a well-handled crossover, the beamwidth of the woofer at crossover will match or nearly match the beamwidth of the tweeter at crossover.
The waveguide allows this trend (transition from omni- to narrow beaming) to be changed. SEOS waveguides are 90 degrees horizontal and 60 degrees vertical, so within their bandwidth (which varies based on the size of the SEOS - SEOS10 has a smaller bandwidth than SEOS24), the beam of sound is narrowed (and also spread if I understand correctly) to the nominal 90x60 pattern. SEOS does this quite well. Above some frequency, the tweeter may begin to beam excessively, and the waveguide may be unable to disperse the sound to the normal pattern. All of that can be seen in this plot, stolen from the hey guys... thread:
Getting the patterns to match in the horizontal plane is important to SEOS designs. Some variation is acceptable - a little waistbanding is fairly common and shouldn't be bad to listen to. If the crossover is higher in frequency than ideal, the pattern of the woofer will be narrower than 90 degrees just below the crossover, and then widen back out to 90 degrees once the waveguide takes over. When measured 45 degrees off-axis, the response will show a dip at the crossover frequency in this case. Potentially then, the lateral reflected energy also shows that dip. The dip is small and dips are easier to listen to than spikes, so waistbanding is acceptable to most people. Wayne Parham (Pi Speakers) has a nice description of a lot of this, here
Now let's start looking at the vertical issues. If the woofer beamwidth was matched to the horizontal pattern of the waveguide at crossover, it can't also be matched to the vertical pattern - since the waveguide is wider than it is tall. If the woofer beam was down to 90 degrees at crossover, now the pattern jumps to 60 degrees in the waveguide. Is that a problem? No, not really.
The real problem is totally independent of changes in the beamwidth. It's an interference pattern due to the fact that there are two acoustic sources at the same frequency. I'm going to copy from rane.com, because the description
is as succinct and complete as I can imagine: "The cancellation nodes are not due to the crossover design, they are due to the vertically displaced drivers. (The crossover design controls where cancellation nodes occur, not that they occur.) The fact that the drivers are not coaxial means that any vertical deviation from the on-axis line results in a slight, but very significant difference in path lengths to the listener. This difference in distance traveled is effectively a phase shift between the drivers. And this causes cancellation nodes -- the greater the distance between drivers, the more nodes." and their picture:
This picture shows why there is a thing called a forward lobe. The direction it points can be changed by moving the drivers relative to one another, or by adjusting the crossover - in particular I think it's the phase effects of the crossover that are most significant here. If you go to the thread at DIYSG where Bill Waslo introduced the Cheap Thrill
, you can read some discussion relevant to this behavior. Bill found that the best response (and therefore what he defines as "on axis,") was above what would normally be seen as "on axis" and explained that this axis could be adjusted by changing the woofer recess in the baffle ("you do the trig").