You can never achieve a good result with a sub.
There is a common belief that using a single subwoofer is sufficient since the human ear cannot detect directionality below 120 Hz. The general consensus is to position the sub in the optimal spot in the room for better bass extension, as explained above -but this couldn’t be more wrong.
The problem with subwoofers isn’t directionality; it’s phase differences and, more importantly, time delays caused by the physical distance between the sub and the main speakers. The only proper way to use a sub is by using two of them, placed either under or beside the speakers. This approach helps minimize phase issues and time delay, effectively integrating the bass drivers into the speaker system.
I have never heard a single subwoofer seamlessly integrated with speakers.
We also always suggest to use minimum 2 subwoofers. Even that we cross over very deep (around 40 Hz).
But of course you also have to take into account the crossover slope.
You mentioned an important point, regarding the phase and time delay, which also varies on the main loudspeaker and the subwoofer by itself. And do not forget the room, because in this deep frequency areas we are talking about wave lengths way bigger than the raw dimensions of the listening rooms!
In order to be able to perfectly adapt the subwoofers to the main loudspeakers, we have integrated in our Divin Sovereign subwoofer controller several tools:
1.) You can choose between 9 different slops and filter functions. 6dB, 12dB Butterworth, 18dB Butterworth, 24dB Butterworth, 12dB Bessel, 18dB Bessel, 24dB Bessel, 12dB Linkwitz, 24dB Linkwitz
2.) You can adjust a delay from 0 to 10710 mm in 1 mm steps.
3.) You can adjust the phase from 0 to 180 degrees in 1 degree steps.
4.) Additionally you can invert the phase.
But someone can write and describe a lot of things. After all hearing is believing!