angles for segmented ESL?

[Andersonix]

I suspect that like almost all other ESL installations, it would be best to absorb the backwave.

Who besides Radio Shack and Janszen/KLH has ever done this? This statement only scratches the surface of your delusions. I'm intrigued!
The two of you seem earnest in your analysis and even seem to have had real world exposure to ESLs, but I think you have whipped each other into a frenzy in this search for the holy grail in ESL design: "Riddance of that pesky backwave."
But I admire anyone who likes ESLs, and I like even more those who would actually build their own. So forgive me for saying this, but I think you're going to end up with a pair of giant ESL corner tweeters. The back pressure in the corners won't allow any bass. I think even a brief internet search for ESL theory will uncover this. I'm sorry I can't back this up with any concrete proof or even point you in the right direction right now, but I hope somebody much more insightful can put you straight.
But I think you should try it anyway. Just leave yourself the option to move the arrays out into the room where you can really let the dipole dispersion pattern make the ESL show its strengths. After ESLs you will never go back to the muffle of regular speakers.

You like quotations? "Those who cannot learn from history are doomed to repeat it."

[I_Forgot]

I think the problem is not whether it would be best to absorb the rear wave, rather the difficulty in doing so over a wide bandwidth. As far as I know, neither RS nor Janszen managed to do it either, except at the highest frequencies.

This is why I prefer flat panels. The rear wave (at least at the higher frequencies) can be controlled by directing it away from the listener through careful positioning of the speakers and listener within the listening space. As soon as you start spraying the audio all over the place, you lose the ability to control it.

As I am always seeking to improve and expand my limited knowledge, may I be so honored as to have a true guru, such as yourself, elighten me as to the nature of my other delusions to which you alluded?

Humbly yours,
I_F

[Brian Beck]

Who besides Radio Shack and Janszen/KLH has ever done this?

Peter Walker (see 1955 Wireless World articles), and Harold Beveridge. Granted few others have tried. I'm not saying this is easy, cheap or even practical, but when have those limitations stopped us DIYers from pursuing perfection?

I think you're going to end up with a pair of giant ESL corner tweeters. The back pressure in the corners won't allow any bass.

Huh? The back pressure in closed box cone woofers doesn't allow any bass? If you had said that the resonant frequency of the diaphragm is increased by the enclosure, I'd have known you understood. If you put any electrostatic panel into an enclosure, whether it’s a box, a corner (for a quarter cylinder), or a flat wall (for a half cylinder) or even a full cylinder as I’m doing, you can use Thiele-Small type analysis. Yes, you must control leaks or you’ll end up with a fourth-order vented cabinet (no thanks).Yes, even electrostatic panels have Fs, Qts, Vas, etc., although the values look pretty strange when you’re used to heavy cone drivers. But the point is that ESLs follow the same physics laws as cone speakers in enclosures, and those certainly can manage to make bass. Remember that the dipole cancellation is the most injurious to bass, and we have an opportunity to eliminate that problem (Quad lover that I am). Now I will tell you from experience that it is difficult to get low enough Fs and Q values for smooth deep bass, so these cylinder sections may be more readily feasible as “almost” full range speakers. But “just tweeters”, no. Worth the effort for almost full-range? Absolutely.

Just leave yourself the option to move the arrays out into the room where you can really let the dipole dispersion pattern make the ESL show its strengths.

Read the thread again. Putting a quarter cylinder in a corner results in effectively no reflections from the side walls - due to symmetry. If it's floor-to-ceiling, the floor and ceiling effectively no longer add reflections (as in any line source). Only the back wall must be considered. Dispersion? Stand up, sit down, move left, move right, it doesn’t matter. The same wavefront is coming at you with almost ideal impulse response. Not so with dipoles or monopoles. Hard to comprehend, I know. Look in an acoustics text about reflective imaging for starters. Symmetry is the magic bullet.

I hope somebody much more insightful can put you straight.

I'm all ears.

After ESLs you will never go back to the muffle of regular speakers.

Agreed!

[Brian Beck]

I think the problem is not whether it would be best to absorb the rear wave, rather the difficulty in doing so over a wide bandwidth.

Well it does take some effort. The question is whether it's worth it or not. For the reasons I've already stated, I think it is. At mid- to higher frequencies where the constructive/destructive cancellation ripples could occur, absorption can be quite effective. The bigger the diameter, the lower the onset of ripple, but also more absorptive material is available in the larger space. Below these ripple frequencies the speaker behaves as a closed box enclosure amenable to Thiele-Small analysis, as I said earlier. At those frequencies absorption is only of secondary importance (just like in a regular woofer box). These are areas that I have been spending some time on.

[Few]

The two of you seem earnest in your analysis and even seem to have had real world exposure to ESLs, but I think you have whipped each other into a frenzy in this search for the holy grail in ESL design: "Riddance of that pesky backwave."

I'm not sure who "the two of you" refers to, but as the initiator of this thread I'd like to point out that my original motivations for corner mounting a quarter cylinder were to eliminate the reflections of the front wave from the ESL off of the room boundaries and to minimize the dependence of the frequency response on the listener's position. Controlling the backwave was not proposed as a "holy grail"; it's just a necessary step toward achieving the primary goals.

As for the fundamental resonance, it's true that it will be affected by corner mounting, but that's not the same thing as restricting the panel to tweeter-duty. If diaphragm material that is more compliant than mylar is used, the free air resonance can be made quite low. Low enough so that the corner-mounting doesn't raise fs too high? I haven't yet done the tests or calculations to find out. However, since my stated goal was to have the ESL operate from a several hundred Hz on up, I think things look promising. My biggest problem now is that I don't yet have the corners necessary to test the idea!

[Andersonix]

It was unfair of me to "attack" you, especially without backing it up with any reasoning, and I'm relieved that I have merely tested your resolve.
But I don't like the analogy you make with sound and light by suggesting that placing the quarter cylinder in the corner will yield a symmetric wave front, as if it were an image in a corner mirror. It seems the sound will be smeared by the early wall reflections, which is what you want to avoid. In fact you now have something like a lens or horn formed by the corner.
And once again I'm sorry I can't give you the actual patent number or anything, but didn't Walker's physics show that ESLs are analyzed completely differently from dynamic drivers, and can't be thought of as being comprised of a piston, motor, springs, and dampers (as S-T does)? Isn't the whole beauty of the ESL in that it comprises an effectively mass less, tensioned diaphragm controlled by (coupled to) the air around it? Where do you get an Fs without mass? The symmetry you seek is across the diaphragm, not up against the wall. I just think you've overlooked something fundamental to ESL analysis (and possibly sound in general)...
I'd like to humbly and cowardly exit from this discussion now, as I hear my mommy calling.

[Few]

Sorry to hear you're exiting, Tosh. I'll offer these comments anyway.

There is very definitely a fundamental panel resonance, and it generally has a pretty impressive Q. You can just tap an undamped ESL panel with your finger and hear the resonance sing out (it's around 100 Hz in my current system). If you increase the diaphragm tension the resonance frequency goes up, as you'd expect on the basis of a mass-and-spring model. The mass is the combined mass of the diaphragm and the air in its immediate vicinity; the spring comes from the compliance of the diaphragm material and the compliance of the diaphragm's air load. The latter is the origin of the "no bass" concerns you voiced previously.

I can't tell if the disagreement about the wall reflections stems from confusion about the front and back waves or something else. The following comments are all restricted to the front wave---the wave that travels directly from the speaker to the listener. I offer them as an alternative to the symmetry arguments helpfully supplied by Brian Beck. They amount to another (perhaps less elegant) way to say the same thing. For simplicity I'll assume an infinitely tall quarter cylinder (or one that reaches floor and ceiling).

The early wall reflections are controlled in the proposed configuration because the wavefronts are always moving parallel to the walls where the wave and walls meet. The key point is that in order to generate a reflection some component of the wave's propagation would have to be perpendicular to the wall. If the previously described quarter cylinder shaped speaker is placed in a corner, and the speaker creates an impulse, the wavefront leaves the front of the speaker as an ever-growing quarter cylinder. If you examine the direction of the wavefront's propagation where the wave is near either of the two walls forming the corner, you find the wave is always moving parallel to the wall's surface. With no component to the wave's propagation perpendicular to the wall there's no reflection.

A complication arises if there's an opening in one of the walls--say an open doorway. In that case the cylindrical wavefront will experience a sudden change in acoustic impedance and the edges of the door opening will act as secondary sound sources. This is all just an overgrown version of the well known diffraction effects encountered when the sound from dynamic tweeters reaches a sharp baffle edge in a conventional speaker. I think it would be desirable to keep such openings---or protrusions from the walls (ie bookshelves)---far removed from the speakers.

Few

[Brian Beck]

Excellent way to explain the concept, Few. I hope you will keep us posted (literally) as your corner speaker comes to life.

[etalon90]

Yes, even electrostatic panels have Fs, Qts, Vas, etc

Can you guess what would be the T&S parameter of an average ESL: (like quad 63 or accoustat model 3)
vas
qts
qms
qes
mms
fs
bl
...

martin

[SY]

BL = 0.

That was easy!