Constant Beamwidth Transducer (CBT) Speakers

[gnarly]

CBT's made for a fun DIY project. Used 24 of the same 3.5" drivers, on an 11 ft radius arc. Simple beginner's CBT/line array project.
Simple other than figuring out how to make a router circle-cutting jig to handle the big arc! lol
I grouped the drivers into six sets of 4 drivers each, for the level shading a CBT requires. Wish I could have done all individually, but ugh..that's a lot of wiring and amp/processing channels.

Two sonic properties of the CBT's really stood out:
First how room placement neutral they were. Just stayed even...nice. And second, how the height of the apparent image center off the floor maybe 3 ft up, didn't change much with distance. I could change from seated and walk up close and the image stayed in the same spot the entire time.

I made baffle that held the 24 drivers removable so I could also mount it on a straight-line box, ala the Murphy corner array style.
It was fun to try to mimic the CBT with delays and level shading. Could get reasonably close, but no cigar. Maybe hurt a little by lack of discrete amplification & processing for each of the 24 drivers. But groups of 4 did at least work pretty well.

Along with trying to mimic the CBT, it was fun to play with the straight line outdoors, moving the apparent acoustic center up and down the line, via delay and/or levels.
Stacked on a sub, it was cool to hear how sound could be made to seem to come from near the top or the line, well over the tops of the heads. Could make for nice small and pleasant backyard party system.

 

[Newman]

Very nice project there, @gnarly. I’m a bit envious.

My understanding of the tech is that your use of 6 banks of 4 drivers would be more than sufficient to get the full acoustic performance. More of an issue would be the driver spacing, which is too great to create the CBT effect above 4-5 kHz. Plus, assuming the drive units are typical of the breed, they might start to individually beam above 6-8 kHz, which is also something Keele was trying to avoid. Nevertheless, great job.

cheers

 

[gnarly]

Very nice project there, @gnarly. I’m a bit envious.

My understanding of the tech is that your use of 6 banks of 4 drivers would be more than sufficient to get the full acoustic performance. More of an issue would be the driver spacing, which is too great to create the CBT effect above 4-5 kHz. Plus, assuming the drive units are typical of the breed, they might start to individually beam above 6-8 kHz, which is also something Keele was trying to avoid. Nevertheless, great job.

cheers

Thanks Newman.
And yep, I agree with your comments.
The issue with any line is always c2c spacing between elements. (and i think for any dang speaker really)

I think a killer CBT needs a line of low freq drivers, with sufficient summed driver displacement to cover the bottom end f-3 to target max SPL,
along with a very tight VHF line that keeps 1/4wl c2c oh so high, and then a mid-range line to bridge those two lines.

The simple 24 driver 3.5"s, has a really beautiful midrange, that works line a line.
They just need lines above and below them, as well.

 

[Curvature]

OTOH see the "Archimedes" EU-funded scientific research project: EUREKA Project E!105 ARCHIMEDES - EUREKA

It was a joint project of Danmarks Tekniske Universitet, Bang & Olufsen and KEF led by Prof. Soren Bech.

From one of the member of the test panels:

I’ve done a lot of testing on the effects of reflections in rooms, and there was a big, big project in Denmark about twelve years ago, with a lot of companies involved in investigating effects of reflections in rooms. I had the pleasure of being a test person, where we could actually simulate the audible effect of the floor reflection, sidewall reflection, ceiling reflection, and so on independently. The single most disturbing reflection in the room is the floor reflection. That is what makes the speaker sound like a radio and not like the actual event. ... The floor reflection absolutely must be handled

Did you read the sources? I don't think you did.

Soren Bech then authored several papers based on the Archimedes system. I mentioned two of them. His conclusions are very limited and we know that he gives strict conditions about how to interpret timbral and spatial modifications by reflections.

Here's the interview you're quoting: https://www.acousticsciences.com/asc-articles/room-acoustics-audios-final-frontier/

We have zero context about Peter Lyngdorf's "radio" comment. Which signal did he hear? We know that speech and noise were used. Under which conditions? Anechoic or with simulated reverberation and multiple reflections? Under anechoic conditions I can see that statement making sense. Otherwise no. Here's the full quote:

I’ve done a lot of testing on the effects of reflections in rooms, and there was a big, big project in Denmark about twelve years ago, with a lot of companies involved in investigating effects of reflections in rooms. I had the pleasure of being a test person, where we could actually simulate the audible effect of the floor reflection, sidewall reflection, ceiling reflection, and so on independently. The single most disturbing reflection in the room is the floor reflection. That is what makes the speaker sound like a radio and not like the actual event. The second worse reflection is the ceiling reflection. Sidewall reflections, if they are sufficiently delayed (more than about five milliseconds) and are left/right symmetrical, can be actually beneficial to the sound. But if your speakers are very close to the sidewalls, you have to kill the side reflections. But do not be too concerned about the sidewall reflections. The floor reflection absolutely must be handled, followed by the ceiling reflection, either by absorption or diffusion.

But I wouldn't take what he says too seriously for a lot of reasons. I do find it amusing, however, that you avoided quoting the middle portion where he notes, conditionally, the benefits of sidewall reflections.

There are no researchers that show that very early reflections are beneficial, and which they are vertically in a normal small room. And no studies that show the vertical reflections are positive in any way. We only have studies that show they have a negtive impact on the sound quality.

I'm surprised you let yourself write something so obviously reactionary and wrong.

The majority of papers we have analyzing reflections are based on spaces other than small rooms, like concert halls. There you can read qualified statements about complex subjective interactions (early reflections, as long as they aren't too strong, increase spaciousness and envelopment, but may decrease clarity and proximity; vertical reflections modify timbre and distance perception, sometimes to listener's detriment, other times to their benefit—think of how integral ceiling reflectors are to the designs of modern halls). However, in Bech's 2019 paper, Perception and preference of reverberation in small listening rooms for multi-loudspeaker reproduction, he says the following:

What we have on small rooms is best summarized in papers by Toole and Olive that many here have read. There are many more who worked on small room acoustics, of course, and I have a small collection of papers that show interesting and contradictory findings. I'll quote just one. Haas, of the "Hass effect", states this in his landmark paper on the effects of reflections in small rooms: The Influence of a Single Echo on the Audibility of Speech

 

[Keith_W]

Lovely speaker there @gnarly! Just two comments:

1. Do you think the drivers should be flush mounted? I realize it's a lot of extra work.

2. CBT's are supposed to be half of an arc, and use the floor as an "acoustic mirror" to create the other half. I wonder what the effect of elevating a CBT off the floor like that would be? (I realize that it's normally on the floor in your listening room in normal use).

I am thinking of making a DIY CBT but I severely lack DIY skills. The thought of creating a curved baffle with all those holes in it for drivers is somewhat terrifying. I suppose you could make all the holes on a flat piece of MDF or ply and then bend it, but wouldn't that create air leaks around the drivers when the baffle is bent? Are there any air leaks, and how did you deal with it?

I am thinking a linear array with digital delays would be easier to construct, but the downside is the tremendous cost of providing so many DAC channels and amps. It would have to be a Ravenna or Dante multichannel DAC, and several of those ganged together no less. I can't think of a cheap way of doing it.

 

[Newman]

There are no researchers that show that very early reflections are beneficial, and which they are vertically in a normal small room. And no studies that show the vertical reflections are positive in any way. We only have studies that show they have a negtive impact on the sound quality.

...I'm surprised you let yourself write something so obviously reactionary and wrong.

Especially since I had, not 5 hours beforehand and just a few posts up, referenced and quoted such a study. A study that Toole describes as the most persuasive evidence on floor bounce in small rooms.

Also, the idea that the floor reflection "makes the speaker sound like a radio and not like the actual event", doesn't even pass the logical 'sniff test'. If true, then a live human speaking in a room will "sound like a radio and not the actual event". Which is ludicrous. Someone should have spotted that at the time, and reviewed the experiment for the possibility of experimental errors including bias (just look at the terminology, 'like a radio').

Conversely, the fact that a person sounds completely natural when talking (or playing an instrument) in a small room with floor bounce, suggests that the same will apply to a loudspeaker. This is supported by what Toole says is the most persuasive evidence. It also passes the sniff test.

cheers

 

[Curvature]

Conversely, the fact that a person sounds completely natural when talking (or playing an instrument) in a small room with floor bounce, suggests that the same will apply to a loudspeaker. This is supported by what Toole says is the most persuasive evidence. It also passes the sniff test.

Right. Bech, Olive and Toole discuss adaptation to room acoustics at length in various places. The ability to adjust and familiarize to certain irregularities is a key feature of our hearing.

 

[youngho]

Right. Bech, Olive and Toole discuss adaptation to room acoustics at length in various places. The ability to adjust and familiarize to certain irregularities is a key feature of our hearing.

Hi, I think that it's possible that multiple factors are getting conflated here. I just came back from a performance at Symphony Hall in Boston (Vivaldi Four Seasons, also Piazzolla's Estaciones Porteñas). The stage is elevated, and I sat in the orchestra section (row S, if you're curious). I also recently attended another performance sitting in the second balcony, near the back wall (Beethoven's Ninth Symphony). In neither situation does the perception of what you seem to discussing as floor bounce apply.

When listening to orchestral recordings, it seems that most are captured from a significantly elevated and/or proximal perspective (or from multiple combinations of the two) relative to an actual member of the audience. Reproduction of such recordings, then, introduces new levels of distortion. Reproducing a close-miked voice via loudspeaker and comparing to a (human) speaker standing near a single loudspeaker location (let alone a human speaker standing between two loudspeakers producing a dual mono recording of a close-miked recording of his or her voice) is another matter.

To simply? The perception of the following may not be equivalent to a listener after adaptation:
1. Person in room
2. Single speaker reproducing person in room (I think you're mostly focussed on #1 and #2 here)
3. Stereo speakers reproducing person in room
4. Single or stereo speakers reproducing person in symphony hall (lots of confounding factors, in my opinion, not just "listener adaptation")
5. Person in symphony hall

 

[Newman]

@youngho that is an acoustically large room. It's different for acoustically small rooms, ie home playback.

 

[markus]

Did you read the sources? I don't think you did.

Soren Bech then authored several papers based on the Archimedes system. I mentioned two of them. His conclusions are very limited and we know that he gives strict conditions about how to interpret timbral and spatial modifications by reflections.

Here's the interview you're quoting: https://www.acousticsciences.com/asc-articles/room-acoustics-audios-final-frontier/

We have zero context about Peter Lyngdorf's "radio" comment. Which signal did he hear? We know that speech and noise were used. Under which conditions? Anechoic or with simulated reverberation and multiple reflections? Under anechoic conditions I can see that statement making sense. Otherwise no. Here's the full quote:

But I wouldn't take what he says too seriously for a lot of reasons. I do find it amusing, however, that you avoided quoting the middle portion where he notes, conditionally, the benefits of sidewall reflections.

I'm surprised you let yourself write something so obviously reactionary and wrong.

The majority of papers we have analyzing reflections are based on spaces other than small rooms, like concert halls. There you can read qualified statements about complex subjective interactions (early reflections, as long as they aren't too strong, increase spaciousness and envelopment, but may decrease clarity and proximity; vertical reflections modify timbre and distance perception, sometimes to listener's detriment, other times to their benefit—think of how integral ceiling reflectors are to the designs of modern halls). However, in Bech's 2019 paper, Perception and preference of reverberation in small listening rooms for multi-loudspeaker reproduction, he says the following:

View attachment 365178
View attachment 365179

What we have on small rooms is best summarized in papers by Toole and Olive that many here have read. There are many more who worked on small room acoustics, of course, and I have a small collection of papers that show interesting and contradictory findings. I'll quote just one. Haas, of the "Hass effect", states this in his landmark paper on the effects of reflections in small rooms: The Influence of a Single Echo on the Audibility of Speech
View attachment 365176

Reading through most of the available literature my conclusion simply is "more research needed". Archimedes was a good start so was Naqvi "The Active Listening Room Simulator".

 

[Bjorn]

Did you read the sources? I don't think you did.

Soren Bech then authored several papers based on the Archimedes system. I mentioned two of them. His conclusions are very limited and we know that he gives strict conditions about how to interpret timbral and spatial modifications by reflections.

Here's the interview you're quoting: https://www.acousticsciences.com/asc-articles/room-acoustics-audios-final-frontier/

We have zero context about Peter Lyngdorf's "radio" comment. Which signal did he hear? We know that speech and noise were used. Under which conditions? Anechoic or with simulated reverberation and multiple reflections? Under anechoic conditions I can see that statement making sense. Otherwise no. Here's the full quote:

But I wouldn't take what he says too seriously for a lot of reasons. I do find it amusing, however, that you avoided quoting the middle portion where he notes, conditionally, the benefits of sidewall reflections.

I'm surprised you let yourself write something so obviously reactionary and wrong.

The majority of papers we have analyzing reflections are based on spaces other than small rooms, like concert halls. There you can read qualified statements about complex subjective interactions (early reflections, as long as they aren't too strong, increase spaciousness and envelopment, but may decrease clarity and proximity; vertical reflections modify timbre and distance perception, sometimes to listener's detriment, other times to their benefit—think of how integral ceiling reflectors are to the designs of modern halls). However, in Bech's 2019 paper, Perception and preference of reverberation in small listening rooms for multi-loudspeaker reproduction, he says the following:

View attachment 365178
View attachment 365179

What we have on small rooms is best summarized in papers by Toole and Olive that many here have read. There are many more who worked on small room acoustics, of course, and I have a small collection of papers that show interesting and contradictory findings. I'll quote just one. Haas, of the "Hass effect", states this in his landmark paper on the effects of reflections in small rooms: The Influence of a Single Echo on the Audibility of Speech
View attachment 365176

I have read Bech's studies. But it's not the only study that indicate the early arriving reflections from ceiling and floor are detrimental. It was well established in studies when acoustic principles were delveoped. But these studies isn't something you can find online.

There's also a difference between accuracy and what can be pleasing to some. Toole investigated more the latter, but the designers of acoustic principles inestigated the first. What's pleasant, for instance late arrivind side wall reflections, is IMO very individual, room and music material depended. Plus, I don't think short listening sessions here work well. Peronally I don't find side wall reflections preferable whether they arrive after 5 ms or 7 ms, but I don't always prefer absorption there either. There many ways to treat those reflections and studies don't take into account all the variables here.

It's very evident and audible when you experience early arriving vertical reflections, and especially if the ceiling is low and sloping. The latter is something you will never find studies to cover completely or perhaps any for that matter. It's impossible for studies to take into account all kinds of ceiling height, angle,s and combined with different width of the room. But there

Quite frankly, I think may here on ASR rely too much on studies and have too little practical experience and stop using common sense in regards to all the variables that studies don't cover. Firstly, it can very audible if it arrives suffiecienty early and from the right angle. Secondly, how much this effects the listening experience in the long run is simply impossbile to quantitfy with researchers.

If you don't see any benefit in the avoidance of vertical reflections in a small room and more or less avidance of the floor bounce, we simply have to disagree. To me that's a huge advantage and is one of major reasons why the CBT works so well.

 

[markus]

I have read Bech's studies. But it's not the only study that indicate the early arriving reflections from ceiling and floor are detrimental. It was well established in studies when acoustic principles were delveoped. But these studies isn't something you can find online.

Please post references otherwise you're again just claiming something that may or may not apply.

 

[Bjorn]

Especially since I had, not 5 hours beforehand and just a few posts up, referenced and quoted such a study. A study that Toole describes as the most persuasive evidence on floor bounce in small rooms.

Also, the idea that the floor reflection "makes the speaker sound like a radio and not like the actual event", doesn't even pass the logical 'sniff test'. If true, then a live human speaking in a room will "sound like a radio and not the actual event". Which is ludicrous. Someone should have spotted that at the time, and reviewed the experiment for the possibility of experimental errors including bias (just look at the terminology, 'like a radio').

Conversely, the fact that a person sounds completely natural when talking (or playing an instrument) in a small room with floor bounce, suggests that the same will apply to a loudspeaker. This is supported by what Toole says is the most persuasive evidence. It also passes the sniff test.

cheers

If the cancellation is deep and broad enough, and which it can be in several cases, that's pretty clear. It can completely render a netrual presentation and the result is a very lean sound with too much emphasis of the upper frequencies. Of course, if it's broad and deep enough. Whether it is that or not will depend also if one is lucky to have peaks in the same area.

I actually sold my center speaker because of this many years ago. It was a Gedlee Abbey speaker but a combination of a floor bounce and possible some other cancellations, lead to a super lean result that sounded very much like a small clock radio. So it was far better to use the front and left, where the cancellation was much less, as phantom center.

Having sufficient level at the upper bass and lower midrange is IMO very important for correct tonality, engaging sound, and listening over long periods of times with various music material without experience listening fatigue. Perhaps you do the AB test yourself one day and listen to both over short and long listening sessions. I have done that with speakers that had the exact same drivers and tuning, but where the difference was the floor bounce. I'm not going back to designs with a floor bounce.

 

[Bjorn]

Please post references otherwise you're again just claiming something that may or may not apply.

The researchers of LEDE designs and other other acoustic principles aren't out there. They were posted as new letters in the 70s and 80s. So I can't link to something that isn't available. But you can find snippets from it and some AES papers. Search for Don Davis and LEDE. And Bech studies are availabe at AES. There are also other, but I don't simply don't have time to look up everything. Besides, this is a CBT thread, isn't?

But it good to use some common sense combined with psycoacoustic researchers. What study can take into account many different ceiling heights with different angles, different widths of room and with various speaker dispersion? Impossible, right?

As an example, this placement and room dimension is absolutely detrimental to speakers with broad vertical dispersion. They sound awful here.

Firstly, the ceiling reflections combined with the close side walls leads the left speaker being predominant and center imgage shiftes strongly to the left. But the worse part is that it leads to some serious frequencies sticking out with harshness and brightness, even when the speaker has no vertical lobing. But a CBT speaker here works really well with no ceiling treatment.

The minimzation of ceiling reflection in such a space is IMO totally necessary and also easy to spot with measurements. But even with normal ceiling height and flat ceiling, minimazation in vertical plane is very audible and a great benefit. There's a clarity, correct tonality and smoothness that broad vertical dispersion speakers simply don't achieve.

 

[markus]

The researchers of LEDE designs and other other acoustic principles aren't out there. They were posted as new letters in the 70s and 80s. So I can't link to something that isn't available. But you can find snippets from it and some AES papers. Search for Don Davis and LEDE. And Bech studies are availabe at AES. There are also other, but I don't simply don't have time to look up everything. Besides, this is a CBT thread, isn't?

But it good to use some common sense combined with psycoacoustic researchers. What study can take into account many different ceiling heights with different angles, different widths of room and with various speaker dispersion? Impossible, right?

As an example, this placement and room dimension is absolutely detrimental to speakers with broad vertical dispersion. They sound awful here.
View attachment 365232

Firstly, the ceiling reflections combined with the close side walls leads the left speaker being predominant and center imgage shiftes strongly to the left. But the worse part is that it leads to some serious frequencies sticking out with harshness and brightness, even when the speaker has no vertical lobing. But a CBT speaker here works really well with no ceiling treatment.

The minimzation of ceiling reflection in such a space is IMO totally necessary and also easy to spot with measurements. But even with normal ceiling height and flat ceiling, minimazation in vertical plane is very audible and a great benefit. There's a clarity, correct tonality and smoothness that broad vertical dispersion speakers simply don't achieve.

Looks like we have a very different understanding of what a scientific study is. All these control room designs from the 70s and 80s are based on trial and error. See Newell "Recording studio design".

 

[Bjorn]

Looks like we have a very different understanding of what a scientific study is. All these control room designs from the 70s and 80s are based on trial and error. See Newell "Recording studio design".

They (SydAudCon and Don Davis) also conducted blind tests and AB comparisons FIY.

But this is really off-topic. If you see no benefit in a speaker that avoids and minimizes reflections from ceiling and floor we are basically worlds from each other in opinions. And why then the interest in a CBT at all?

 

[markus]

They (SydAudCon and Don Davis) also conducted blind tests and AB comparisons FIY.

But this is really off-topic. If you see no benefit in a speaker that avoids and minimizes reflections from ceiling and floor we are basically worlds from each other in opinions. And why then the interest in a CBT at all?

You're missing the point: https://www.audiosciencereview.com/...th-transducer-cbt-speakers.12060/post-1954377

 

[gberchin]

If I succeed, I'll report my results here. I don't think that Don will mind.

Fortunately, I left a Matlab/Octave script that provided enough information to get me back on-track.

First, a bit of context:

In 2021, Don Keele sent me a copy of this paper, https://www.xlrtechs.com/dbkeele.com/PDF/Keele (2002-10 AES Preprint) - CBT Paper2.pdf, and asked me if I could help with the design of the delay filters described within. That paper details how the performance of a curved CBT array can be approximated by a straight CBT array, if the signals feeding the array elements are delayed in time. Normally, one thinks of delay in digital systems in terms of integer numbers of samples, but the delays required for straight-line CBT arrays involve fractions of samples. (Delays longer than a sample period are implemented as the appropriate number of integer sample delays plus the remaining fractional parts.) In summary, successful implementation of the concepts presented in Keele's paper requires fractional-sample delays, effective over as much of the audio band as possible.

There are multiple ways to implement fractional-sample delays; some are very accurate but also very complicated. Probably the simplest approximation of delay utilizes allpass filters, and this is the method proposed in Keele's paper. The problem, though, is how to design those allpass filters for high accuracy, broad bandwidth, and simple implementation.

Fortunately, way back in 1985 or so, I created a system identification algorithm that I named "Frequency Domain Least Squares" (FDLS). This algorithm determines the transfer function associated with an arbitrary (within reason) magnitude/phase frequency response. And of greater relevance, in 2018 I created a variant of FDLS that determines the allpass transfer function associated with an arbitrary (within reason) phase response. I call that variant "FDLS_allpass".

At this point I should mention a unique characteristic of IIR digital allpass filters, exploited by FDLS_allpass: The numerator and denominator coefficients of a digital allpass filter are identical, but in reverse-order. That is to say, if the numerator is ...
b0 + b1z^(-1) + b2z^(-2) + ... + bNz^(-N)
then the denominator is the same but in the reverse order ...
bN + ... + b2z^(-(N-2)) + b1z^(-(N-1)) + b0z^(-N)
This halves the number of coefficients to be implemented.

It turns out that FDLS_allpass is very well-suited to the task at hand. For example, I arbitrarily chose one of the delays shown in Table 1 of Keele's paper, 13.86 microseconds, and put FDLS_allpass to work. I set it to create a 10th-order allpass filter exhibiting that delay from 50 Hz to 24 kHz in a 48 kHz sampling context. The graphics below show the results. The upper figure shows the big picture. The lower figure shows detail of the upper figure, with the green lines indicating ±1% delay error. Note that the delay error does not exceed 1% until well beyond 20 kHz. Lower-order filters behave similarly, but start to diverge from the desired value at lower frequencies.

And for anyone who is interested, here are the coefficients that generated the response shown:
B =
0.03495862202512633 (b0)
3.241123242061795 (b1)
41.80822069766062 (b2)
213.8704208921733
566.9862913036701
867.7409808502701
797.2467426424935
436.4562319420752
134.3644482816463
20.13203387159336
1 (b10)
This should be decomposed into second-order sections for implementation. Allpass poles and zeroes occur as pairs along the same angle from the x-axis, the pole at radius R and the zero at radius 1/R.

FDLS_allpass.m, along with a utility script that creates and formats input data for it, are available from me as Matlab/Octave scripts. Send a PM if interested.

- Greg Berchin

 

[gnarly]

Lovely speaker there @gnarly! Just two comments:

1. Do you think the drivers should be flush mounted? I realize it's a lot of extra work.

2. CBT's are supposed to be half of an arc, and use the floor as an "acoustic mirror" to create the other half. I wonder what the effect of elevating a CBT off the floor like that would be? (I realize that it's normally on the floor in your listening room in normal use).

I am thinking of making a DIY CBT but I severely lack DIY skills. The thought of creating a curved baffle with all those holes in it for drivers is somewhat terrifying. I suppose you could make all the holes on a flat piece of MDF or ply and then bend it, but wouldn't that create air leaks around the drivers when the baffle is bent? Are there any air leaks, and how did you deal with it?

I am thinking a linear array with digital delays would be easier to construct, but the downside is the tremendous cost of providing so many DAC channels and amps. It would have to be a Ravenna or Dante multichannel DAC, and several of those ganged together no less. I can't think of a cheap way of doing it.

Thank ya Keith_W,

1a. For sound? Not really.
The little TC-9s I used, have a mounting flange only about 3-4mm thick. Even 20kHz waves can bend around that. Besides they can't begin to play that high anyway.
If diffraction is a concern, I think I'd rather have felt stips running along side the drivers, on the front of the speaker, than flush mounting.....for SQ.
Also, the diffraction will be the same up and down the line (using single small full-rangers, so should be largely correctable..

1b. For looks? Yeah. If that's part of the DIY fun, I say go for it !

2. The ground plane CBT I built, is the 36 degree arc version, so 1/10th of a full circle. I think ground placement and the recommended Legendre shading coefficients are integrally tied together...so my thoughts are it does need to be on the ground. But I don't know that for sure.

I see a 78 degree flown example on Keele's website, and I know he has a bunch of work out on flown line arrays in general.
I think that's what you'll need to study if you want to fly a line. My guess again, is that it may not be a CBT that fits best, but maybe some hanging J or something. Out of my depth here really.

Surprisingly, making the driver baffle was not that hard. I laminated 2 pieces of softer core, 6mm, furniture grade birch plywood together. Straight 12mm" stuff, particularly baltic-birch just would not bend easily enough. Cut baffle to width and length, lay it down flat, mark the hole centers an have at it. Then roundover outer edge. Didn't even take that long.
Hardest thing again, was making the curved arc sides. To get the edges smooth a used a router, with a big ass homemade circle jig. A jig saw would work, but probably require a lot of hand sanding to get the edges smooth enough for the baffle to mount tightly.

To avoid air leaks I made rubber o-rings that fitted nicely on the TC9's. I little math showed the 3.5" drivers on the 7ft long arc, made for about 1/2mm air gap against the curvature. So I used rubber cord 1/16th" of 1.6mm for the o-rings. Impedance and stethoscope proved they sealed up fine.
Oh, and as you could see in picts...one big chamber for all drivers...why make it hard ?

The most channels I would entertain per speaker is 12 I think. Not sure having all 24 would add that much. I'd like to have used 8 banks of three, but no way to connect three 8 ohm drivers for an acceptable load.
Qsys made it really easy, and used qsc cx168 8 Ch amps were going for about $250 a piece. If I ever move to 12 channels, I'll look into some kind of chip amp. And heck if the amps are cheap enough, Qsys setup could handle the processing and I/O for all 48 drivers...if i want to go nutz.

Hope this has helped. Really was a fun project....and sounded great. Maybe i need to pull em out of storage lol

 

[TimVG]

Is there a practical approach to determing the shading levels for a given arc? Looking up CBT designs I see quite a bit of variation in the shading used for a given arc, in the number of banks but also the relative dB.