How does adding a second subwoofer improve your systems SQ?

Atmasphere, in general I agree with what you say with point source speakers that are not digitally corrected and time alligned. However when it comes to linear arrays particularly tall ESL dipoles the situation changes somewhat. If the subwoofer system does not want to get loss under the linear array it also has to radiate like a linear array. This requires a driver every 5 feet or so with the line ending at wall boundaries. If the system were on a long wall this might require more than four units. Dipole ESLs just do not do well under 100 Hz. As you mentioned crossing up higher than 80 Hz without digital correction won't work well. You will always know there is a sub woofer down there. But with time and phase alignment you can go up higher. I cross at 125Hz 4th order and unless you open your eyes you would never know there was a separate subwoofer system and because the sub woofers are forming a linear array the relative volume between the subs and satellites does not change with distance. The linear array also minimizes room effects which allows me to do room correction with much less power. The the resulting improvement in performance of the ESLs at volume is imminently noticeable as is the marked improvement in head room. It's like adding a turbocharger to your engine. 

Mike  

I should also note that I have never used digital correction with a point source system. I have to believe that subwoofer integration would be easier and better. Although I thick you could get away with a higher crossover the benefit would be questionable as the woofer in the satellite has a very limited range whereas with a one way ESL the entire frequency band is affected by the long excursions bass requires particularly at volume. When a very low note comes along say 18 Hz at volume you can actually hear the music flutter. 

@markj941,
good sum summary.  i just added two REL t9i to my system and am very happy with the sound.  they integrate very well with my large british monitors compared to two other sub brands i tried. 
an important considesrtion is distance from wall behind them.  closer than 8 inches created strong peaks in the response.

You are getting a just sample of what’s going on down there, you are drawing conclusions about the Roger Waters track with regards to hearing it with two L and R subs, it’s obvious. Because if you did you wouldn’t be saying what you just said.

It acts the same way on my main system, which has bandwidth to 20Hz out of the main speakers (Classic Audio Loudspeakers Project T3.3).

It appears that bass traps have their cultists too. The simple fact is they are not always practical. A local customer of mine has been using them for years; I finally got him to try a DBA and it solved his bass issues which he's been fighting for over 20 years. His room is arguably the most treated room I've seen anywhere. He was pretty adamant about how great they were until the DBA showed up.  At this point he's running only about 1/5th of what he had before. In my room I simply don't have the space to place them at all, but adding a pair of subs (thus creating a DBA) is easy since they can hide under a couple of tables in the space. No way could I get bass traps to do the same job in my room, and the GF won't stand for it anyway. Science works so much better than myth for solving these problems.

Hi markj941,
I added a set of  REL subs to my system with floor standing speakers and It was a great improvement .Most notable was that the overall soundstage was cleaner and there was a much greater sense of depth. The bass was more authoritive, the details were extended especially in the midrange. Drumskins, toetapping, broken guitar strings, etc. all clearly audible. My system is set up in my livingroom, and I do not have any real room treatments to speak of. I dream of having a dedicated room one day, but the addition of the subs definately elivated my system to the next level.  Mark Knopfler's Private Investigations is also a good comprarable. 

Good Luck