Yes, it's not due to the fr shape of the individual drivers at all. It is simply a phase shift of one driver relative to the next one because of the time difference.
Take one driver making a 85Hz sine, and take another driver making a 85Hz sine, both equally loud. If one driver is about 2 meter to the side of the other driver but the same distance to the listener, let say both drivers are 4m from the listener, the the two drivers / sines are perfectly in phase relative to the listener so they add up making the resulting sine 6dB louder.
Now if we move to the side of both speakers, the relative distance changes. Let's say we are now 3 meters from driver 1 and 5 meters from driver 2. Both drivers are still playing the same sine, but now the sine from speaker 1 arrives before the sine from speaker 2. And in this case the sine from speaker 2 arrives about 1 second / (340m / 2m) = about 6ms later. If the frequency was 340m / 2m = 170 Hz then the sine would be a full wavelength later so be in phase. But the frequency is half this, 85Hz, so the sine that arrives later from driver 2 is exactly out of phase with the earlier sine from driver 1. So they cancel out (well, they would if they didn't have an SPL difference, but even in this example they mostly cancel out).
So you were thinking too difficult (minimum phase logic only works when time is not involved, like in this example or like with reflections etc), but this is the most easy thing
Okay, I misunderstood what you meant when you wrote, "I was talking about the power response and the cancellation axis of the crossover." You were talking about the locus of points where the two outputs are out of phase, analogous to the nulls that occur in the vertical polar response of a two-way speaker. In this case, both above the horizontal and below the horizontal there is a locus of points where the distance to one driver is greater by one-half wavelength than the distance to the other driver, with respect to a specific frequency. These loci, both above and below the horizontal, define the upper and lower boundaries of the main lobe for a given frequency.
So now let's see. At 80 Hz the wavelength is 4.29 m. A half-wavelength will be 2.14 m, so at all points that are 2.14 m closer to either the woofer or the subwoofer than to the other, an 80 Hz tone will vanish. We are on the same page, and you correctly pointed out that the dip at 80 Hz along this locus will not be total cancellation because of the many reflections and re-reflections from the walls. So most likely it will be a mild dip, unless you are so close to both the woofer and the subwoofer that the direct wave from each is highly dominant over the reflections. I'm not sure I followed the rest of it it, but I will note that cancellation additionally occurs, to varying degrees, for all frequencies at which both sources are making a significant contribution to the sound pressure. And the two wavefronts do not have to be exactly 180 degrees out of phase. This is what I thought you were alluding several posts back when you first mentioned 1/4 wavelength, i.e., that when the phase difference becomes as great as 90 degrees, the cancellation is strong enough to make a difference.
Several posts back you wrote, "So in a precise setup you'd want the center of the subwoofer driver to be no farther away than about 1m from the center of the speaker woofer when crossing at 80Hz in order to get an even power response / room response around the crossover freq." Perhaps this is a good estimate, but it isn't an exact thing, to my way of thinking, owing to the fact that the cancellation itself is not limited to the exact crossover frequency (although it is strongest there) and to the fact that it occurs to milder degrees for phase differences less severe than 180 degrees. But if you take 180 degrees and the exact crossover point as the worst case and figure out how close together the woofer and subwoofer should be, such that the nulls that define the main lobe will be adequately far apart, this works of course, and I suppose that this is what you did. But if I compare it to the problem of vertical separation of a woofer and tweeter in a two-way speaker, where the maximum allowed separation depends on the wavelength at the crossover point and also on the angular distance above and below the horizontal you require for the cancellation loci, i.e., the minimum allowed angular spacing between the two loci, it would seem that by analogy the maximum allowable spacing between the woofer and subwoofer will depend on what you choose for the angular width of the lobe, measured horizontally of course.
I want to say plainly that I do not take a position on which of the two concerns is the stronger concern. It seemed to me that it isn't possible to deal with both simultaneously and I pointed this out. The majority opinion here is clearly that mitigation of room modes is more important. Although it also occurs to me that room modes exist for all frequencies where 1/4 wavelength is shorter than the longest room dimension, i.e., the only wavelengths where standing waves don't set up are wavelengths more than four times greater than the greatest room dimension. Somewhere in the lower bass they start, and they don't stop once you've transitioned from the subwoofer to the woofer, or at any point. At 500 Hz the wavelength is about .7 meter, so if the distance between any two opposing walls is an exact integer multiple of .7/4 meters, there will be room modes for 500 Hz. I suppose there is a reason why this matters more with low bass than it does with higher frequency, but I need to think about this some more before I will have a good understanding of why.
One thing I'm still confused about, which is partly why I misunderstood what you meant before, is this:
"The above story is the same as the tweeter - midwoofer crossover dips we see in all Amir's measurements (other than the coaxials), those are already bad enough but the effect of this is much worse when it is in the bass frequencies like with a sub that is placed far away from the speaker."
This is what I was getting at, or trying to, a couple of posts back. I don't yet understand why it is that when two drivers' outputs sum flat in the on-axis response there is a strong dip at the crossover frequency in the off-axis response. This is probably one of those things that becomes obvious once you understand it, but at the present I'm still trying to understand exactly why this happens.
