Hi there! I have committed myself to building one, at least as far as reading up on them, and just bought about $100 worth of lumber at Home Despot. I split this off from my earlier thread since I successfully (?) have built a Bass Cannon, although it was not a clone of the Bose but just a Sonotube with a 12" woofer stuck in one end. It works great, but...
I had been hoping to pioneer Carpentry-Free (TM) subwoofers, but this poses a challenge. I am a reasonable man (and lazy too) and here is what I came up with: Look guys, not all of us have state of the art factories or even a circular saw at our disposal. What I've done is this:
Have a vague plan to build an enclosure. Details to follow. It will be a very simple enclosure, and might even work. My point is to make the assembly as easy as possible. It is made with nearly off the shelf parts, thus requiring a minimum of cutting. The major cutting was done for free at Home Depot. Here is my parts list:
1 sheet (4x8) plywood, your choice. I got 1" pine, have it cut to three long rectangles, each 18" wide x 8' long. These are the "front", "back" and speaker mounting doohickey (I'll call it a "diagonal").
2x boards, 1" x 12" x 8'; these are the left and right sides.
1x board 1" x 12" and long enough to make the top and bottoms. I will have to cut this one...
I don't have a diagram, I will upload a photo soon. Right now I am just nailing it together. Screwing & glueing later if it looks promising.
I am more or less copying Cowan's 30 Hz horn, here is a link to it:
Tapped Horn Experiments
Mine will have dimensions of roughly 8 feet high, 1 foot deep, 18" wide. To be determined, the exact cuts for the diagonal (speaker mounting board) and also the port. Most likely the port will go on the "bottom" (near the driver); it would work as well on its side too I guess.
Rather than cannibilize my existing driver, I am soliciting suggestions for the best driver for my soon-to-be enclosure.
I had been hoping to pioneer Carpentry-Free (TM) subwoofers, but this poses a challenge. I am a reasonable man (and lazy too) and here is what I came up with: Look guys, not all of us have state of the art factories or even a circular saw at our disposal. What I've done is this:
Have a vague plan to build an enclosure. Details to follow. It will be a very simple enclosure, and might even work. My point is to make the assembly as easy as possible. It is made with nearly off the shelf parts, thus requiring a minimum of cutting. The major cutting was done for free at Home Depot. Here is my parts list:
1 sheet (4x8) plywood, your choice. I got 1" pine, have it cut to three long rectangles, each 18" wide x 8' long. These are the "front", "back" and speaker mounting doohickey (I'll call it a "diagonal").
2x boards, 1" x 12" x 8'; these are the left and right sides.
1x board 1" x 12" and long enough to make the top and bottoms. I will have to cut this one...
I don't have a diagram, I will upload a photo soon. Right now I am just nailing it together. Screwing & glueing later if it looks promising.
I am more or less copying Cowan's 30 Hz horn, here is a link to it:
Tapped Horn Experiments
Mine will have dimensions of roughly 8 feet high, 1 foot deep, 18" wide. To be determined, the exact cuts for the diagonal (speaker mounting board) and also the port. Most likely the port will go on the "bottom" (near the driver); it would work as well on its side too I guess.
Rather than cannibilize my existing driver, I am soliciting suggestions for the best driver for my soon-to-be enclosure.
My advice next time. Skip Home Depot ply. Baltic birch (18mm) isn't that much more expensive from a good supplier and it's worlds better. That's all.
It would have been a lot easier to help if you hadn't started building before asking for help.
For example, I could have told you that it's quite easy to come up with a design if you start with a list of goals or a given driver. It's much much harder to come up with a driver that will work well in a pre-determined box.
Also, it would have been a lot better with a depth of 18 inches and a width of 12 inches. Your aspect ratio (especially in the throat) is going to be ridiculously high for no real good reason, other than the fact that you pre-determined the dimensions with no forethought.
This is going to be a challenge, but not a fun one for me. Someone will probably help out though, lots of people already have hundreds of design files and one of them might fit your dimensions. Good luck.
For example, I could have told you that it's quite easy to come up with a design if you start with a list of goals or a given driver. It's much much harder to come up with a driver that will work well in a pre-determined box.
Also, it would have been a lot better with a depth of 18 inches and a width of 12 inches. Your aspect ratio (especially in the throat) is going to be ridiculously high for no real good reason, other than the fact that you pre-determined the dimensions with no forethought.
This is going to be a challenge, but not a fun one for me. Someone will probably help out though, lots of people already have hundreds of design files and one of them might fit your dimensions. Good luck.
What port are you speaking of? TH's don't use ports. (Unless we're referring to one of danley's designs....) and that's more of a duct.
Agree with everybody. I'm impulsive. I waste some time and money. But I learn something...maybe.
What port? The one that lets the sound out of the box 🙂 At least with some designs (like the Trans-Flex) you can experiment with the size of the port for the best tuning.
What port? The one that lets the sound out of the box 🙂 At least with some designs (like the Trans-Flex) you can experiment with the size of the port for the best tuning.
Ok, I confess. I could not wait. I tore the driver from my helpless Sonotube and installated it in my new monstrosity. Letting the cualk dry overnight and...it works, but major rattles. I'm guessing that internal bracing would help. So that is on the to-do list. Also: modify design so that removing a panel is easier (or possible?)
If nothing else, perhaps this will become a tutorial on how to NOT build a TH 🙂
If nothing else, perhaps this will become a tutorial on how to NOT build a TH 🙂
Well, I have to admit I am curious. If you want I can simulate what you have. At the very least I need the driver specs, the throat area and the mouth area.
Ideally measured (not published) specs for the driver and simple sketchup drawing of the box would help (attach the skp file, not a picture of the sketchup screen). If you can't (or don't want to) provide these items the sim won't be as accurate as possible.
I'm also interested in your other design. I haven't followed the other thread so I'd need a quick drawing or explanation of the dimensions of your tube and where the driver attaches.
Maybe you are really lucky and you've got two winning designs. It's possible.
Ideally measured (not published) specs for the driver and simple sketchup drawing of the box would help (attach the skp file, not a picture of the sketchup screen). If you can't (or don't want to) provide these items the sim won't be as accurate as possible.
I'm also interested in your other design. I haven't followed the other thread so I'd need a quick drawing or explanation of the dimensions of your tube and where the driver attaches.
Maybe you are really lucky and you've got two winning designs. It's possible.
While simple is usually good, there is nothing simple about horn speakers. Since they are complex (as in complex numbers, real and reactive) acoustic impedance transformers, you may want to study AES Journals Vol I+II for details on finding our which drivers may be even suitable to expect good results with. A Peerless with a fs of 18Hz is the opposite candidate for a horn - build a transmission line with it. The suggested tapered horn is actually more similar too a TL than a real horn. It also lacks a compression chamber. As a rule of thumb to get a better match of horn reactance to speaker (acoustic) impedance, seek drivers with high Fs (40-80Hz), low Qts (0.15-0.25).
You can modify it by enclosing one side of the speaker, or even porting one side to lower Q, as it will increase in a sealed enclosure. Most notably, this is how to adjust driver to match the legendary Klipsch corner horn. You must pick a horn cut-off below fs, otherwise your speaker impedance will never match the horn reactance (the annulling condition). Second, heuristically, compression chambers with a small Vb compared to Vas (1/10th or less) and throat openings between 30 to 60% of S(D) have worked well, but to be exact, you must go through the acoustic impedance analysis. Anyway, I am sure you weren't up for pursuing doctorate degree on this, but it is amazing pleasure to experience a well-designed horn.
You can modify it by enclosing one side of the speaker, or even porting one side to lower Q, as it will increase in a sealed enclosure. Most notably, this is how to adjust driver to match the legendary Klipsch corner horn. You must pick a horn cut-off below fs, otherwise your speaker impedance will never match the horn reactance (the annulling condition). Second, heuristically, compression chambers with a small Vb compared to Vas (1/10th or less) and throat openings between 30 to 60% of S(D) have worked well, but to be exact, you must go through the acoustic impedance analysis. Anyway, I am sure you weren't up for pursuing doctorate degree on this, but it is amazing pleasure to experience a well-designed horn.
Will have to get back to you guys with hard data. Have to take out some time to catch up on academic reading 🙁
Will have to get back to you guys with hard data. Have to take out some time to catch up on academic reading 🙁
I don't think reading is going to help much here. This is a job for simulations. I did notice this quote from your other thread.
... I want to "fiddle about" as Uncle Ernie said and who needs those stinking sims???
Tapped horns are very intolerant to "fiddling about" design routine. There is a method that GM uses, which utilizes classic horn theory and some custom modifications to achieve good designs, but figuring that out isn't going to be a casual afternoon read, it's going to take a long time. The only other alternative you really have is a simulator or someone who knows how to use one. Otherwise, fiddling about is usually going to give you a product that can be easily matched or beat by a simple ported box much smaller than your tl or horn.
For your information, I have put together a couple of posts concerning your sonotube tl and your current tapped horn project. Hopefully you won't see this as discouraging, instead look at it as a good reason to learn to simulate.
So... curiosity got the best of me again. A quick skim over your previous thread shows you are using this driver - http://www.tymphany.com/files/XXLS-P830845 Rev1_0.pdf - and you don't have measured specs, only published specs so that's what I used.
First I simulated your sonotube tl, which I believe was 10.5 feet long and I assume you used 12 inch interior diameter tube with the driver loaded on one end. (Small changes in tube cross sectional area won't make much difference.)
Picture 1 - Hornresp inputs, check my work for mistakes
Picture 2 - displacement shown at xmax, and showing a ~25 hz tuning
Picture 3 - response in the middle
Picture 4 - response on terminus end
Picture 5 - response on driver end
I saw that you mentioned it could play 15 hz, and I believe you even said it could do 12. It can, obviously, but since it's about an octave below tuning at that frequency it's about 25 db down at that point. And for best performance you should have a high pass filter to protect it below tuning, so technically it should be inaudible at 12 hz.
I included 3 response graphs to give you an idea of how response can change depending on where you stand in relation to the sub. Most subs are not this variable depending on position, but since your driver and terminus are so far apart this is what you get. Depending on where you are when you measure you will get wildly different response curves. The room will even this out to some degree (and insert it's own wild influence) but it's still pretty erratic.
Based on the variable response depending on your location relative to the sub, the wild response no matter where you stand, and the fact that this doesn't go much louder than a much smaller ported box with the same driver, this design isn't my cup of tea. A bit of stuffing would help to even out the response a bit though. If you wanted to try that I would put it near the driver end, none in the terminus end, and fill to taste.
First I simulated your sonotube tl, which I believe was 10.5 feet long and I assume you used 12 inch interior diameter tube with the driver loaded on one end. (Small changes in tube cross sectional area won't make much difference.)
Picture 1 - Hornresp inputs, check my work for mistakes
Picture 2 - displacement shown at xmax, and showing a ~25 hz tuning
Picture 3 - response in the middle
Picture 4 - response on terminus end
Picture 5 - response on driver end
An externally hosted image should be here but it was not working when we last tested it.
I saw that you mentioned it could play 15 hz, and I believe you even said it could do 12. It can, obviously, but since it's about an octave below tuning at that frequency it's about 25 db down at that point. And for best performance you should have a high pass filter to protect it below tuning, so technically it should be inaudible at 12 hz.
I included 3 response graphs to give you an idea of how response can change depending on where you stand in relation to the sub. Most subs are not this variable depending on position, but since your driver and terminus are so far apart this is what you get. Depending on where you are when you measure you will get wildly different response curves. The room will even this out to some degree (and insert it's own wild influence) but it's still pretty erratic.
Based on the variable response depending on your location relative to the sub, the wild response no matter where you stand, and the fact that this doesn't go much louder than a much smaller ported box with the same driver, this design isn't my cup of tea. A bit of stuffing would help to even out the response a bit though. If you wanted to try that I would put it near the driver end, none in the terminus end, and fill to taste.
Now the tapped horn. Same driver, shown at xmax for the first sim, and same Eg for all the rest (although the last 3 are slightly past xmax). Since you didn't give any internal dimensions I just guessed. You've got about 1220 cm total cross sectional area, so I simulated it with different throat and mouth areas that add up to 1220 cm and a 16 foot length. Note that these sims are not an exact match to your box but well within reason to get an idea of what's going on.
First, shown with 120 cm throat and 1100 cm mouth.
Now with 220 cm throat and 1000 cm mouth.
Now with 320 cm throat and 900 cm mouth.
And finally with 420 cm throat and 800 cm mouth.
None of these have really great response curves and none of them get any louder than a ported box of half the size with the same driver. So that isn't a good sign. Also, the aspect ratio in the throat is extremely high.
In each case, comparing the tuning dip in the displacement curve to the low frequency knee in the response graph shows that you are not getting good output down to tuning, as you should. This driver doesn't work well in that box, no matter what you do with the internal divider.
First, shown with 120 cm throat and 1100 cm mouth.
An externally hosted image should be here but it was not working when we last tested it.
Now with 220 cm throat and 1000 cm mouth.
An externally hosted image should be here but it was not working when we last tested it.
Now with 320 cm throat and 900 cm mouth.
An externally hosted image should be here but it was not working when we last tested it.
And finally with 420 cm throat and 800 cm mouth.
An externally hosted image should be here but it was not working when we last tested it.
None of these have really great response curves and none of them get any louder than a ported box of half the size with the same driver. So that isn't a good sign. Also, the aspect ratio in the throat is extremely high.
In each case, comparing the tuning dip in the displacement curve to the low frequency knee in the response graph shows that you are not getting good output down to tuning, as you should. This driver doesn't work well in that box, no matter what you do with the internal divider.
I don't want to bore with with 4 consecutive posts but here's what I would suggest.
Take my Hornresp inputs, make sure they correspond correctly to your physical build (the lengths and cross sectional areas might need to change a bit) and try different drivers. This approach may take a few days but there will be a driver that works well in there.
Otherwise, since it isn't glued up yet you can ask for help in designing something better (and preferably with a different driver). This will require making some cuts to the wood you have but it will fix some things like the extremely high throat aspect ratio. It only takes a couple of minutes to do a simulation and not much longer to do a simple single fold job, but it could take quite a bit longer to try to retrofit your existing box with a compatible driver, and it will never be as good as it could have been due to things like the throat aspect ratio.
Again, good luck.
Take my Hornresp inputs, make sure they correspond correctly to your physical build (the lengths and cross sectional areas might need to change a bit) and try different drivers. This approach may take a few days but there will be a driver that works well in there.
Otherwise, since it isn't glued up yet you can ask for help in designing something better (and preferably with a different driver). This will require making some cuts to the wood you have but it will fix some things like the extremely high throat aspect ratio. It only takes a couple of minutes to do a simulation and not much longer to do a simple single fold job, but it could take quite a bit longer to try to retrofit your existing box with a compatible driver, and it will never be as good as it could have been due to things like the throat aspect ratio.
Again, good luck.
No, the reading is for a university course. As for my TH, it is taken apart right now, offering a chance to (ahem!) make throat wider than zero and also to brace it extensively. I should probably learn to use a sim myself. "Discouraged"? Not at all. This is a cheap way to feed my tinker urge (wasted time perhaps not included.) Unfortuantely I don't have a draw program, I can do a pencil sketch and post it in a few days.
"Just a guy": I don't deny my TH is a mess right now, but it's hard to screw up a Sonotube TL isn't it? (As I implemented mine.) Transmission line practice doesn't get much simpler than long tube + driver at (or near) end 🙂
As I show in the next post the "real world" performance is pretty good (?) especially considering the ease of making it. To date, the Sonotube TL is the only truly Carpentry-Free(TM) sub I am aware of 🙂
I can't enlarge your screen shots very much for some reason. Request: would you send me the hornresp file you used? I think it's time I learn to use this program. I can model before I meddle. And in my spare time, read and write for Spanish Literature. Anybody have a tutorial for medieval or caribbean writings? 🙂
"Just a guy": I don't deny my TH is a mess right now, but it's hard to screw up a Sonotube TL isn't it? (As I implemented mine.) Transmission line practice doesn't get much simpler than long tube + driver at (or near) end 🙂
As I show in the next post the "real world" performance is pretty good (?) especially considering the ease of making it. To date, the Sonotube TL is the only truly Carpentry-Free(TM) sub I am aware of 🙂
I can't enlarge your screen shots very much for some reason. Request: would you send me the hornresp file you used? I think it's time I learn to use this program. I can model before I meddle. And in my spare time, read and write for Spanish Literature. Anybody have a tutorial for medieval or caribbean writings? 🙂
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Here is a sweep of the Sonotube TL.
Since you are helping with the sims already, here is a sweep I did last month of the "Ijit Sonotube" for lack of a better name. You already have the correct techncial data from the other thread. With some EQ for the peaks only, I get pretty flat response in-room. Notable: over on HTS (similar thread), w/o EQ I get similar peaks and troughs with just the pair of Bose 901s. Probably the room is at fault (a prime suspect!).
Since you are helping with the sims already, here is a sweep I did last month of the "Ijit Sonotube" for lack of a better name. You already have the correct techncial data from the other thread. With some EQ for the peaks only, I get pretty flat response in-room. Notable: over on HTS (similar thread), w/o EQ I get similar peaks and troughs with just the pair of Bose 901s. Probably the room is at fault (a prime suspect!).
Attachments
"...learn to use a sim..."
Post #14
Hi Soldermizer,
Post #14: "...I should probably learn to use a sim myself..."
I second that sentiment, and I recommend Hornresp by David McBean whole heartedly.
Just in case I'll attach four different enclosure models for the Peerless 830845, import into Hornresp, and start messing around. 🙂
Regards,
Post #14
Hi Soldermizer,
Post #14: "...I should probably learn to use a sim myself..."
I second that sentiment, and I recommend Hornresp by David McBean whole heartedly.
Just in case I'll attach four different enclosure models for the Peerless 830845, import into Hornresp, and start messing around. 🙂
Regards,
Attachments
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No, the reading is for a university course. As for my TH, it is taken apart right now, offering a chance to (ahem!) make throat wider than zero and also to brace it extensively. I should probably learn to use a sim myself. "Discouraged"? Not at all. This is a cheap way to feed my tinker urge (wasted time perhaps not included.) Unfortuantely I don't have a draw program, I can do a pencil sketch and post it in a few days.
Is the throat really zero? (It comes to a point?) That probably isn't ideal. But I was talking about aspect ratio, which is something different. Large aspect ratios are not a good thing. For example, if your throat area was 1 cm by 45.72 cm (18 inches), the aspect ratio would be 45.72:1, which is extremely high. If your throat area is zero by 45.72 cm then your aspect ratio is infinity.
If wood is cheap to you then tinker away. I don't have a lot of extra cash and I don't really like the construction process, so I spend a LOT more time reading, researching and simulating than I spend building. But I do strongly recommend simulation for you, it's very easy and fast once you get used to it.
"Just a guy": I don't deny my TH is a mess right now, but it's hard to screw up a Sonotube TL isn't it? (As I implemented mine.) Transmission line practice doesn't get much simpler than long tube + driver at (or near) end 🙂
As I pointed out, having the driver and the terminus so far apart is problematic. You get different measured results depending on where you are standing in relation to the sub. Your room probably evens this out to some extent but if you measured it outside it would be very clear.
Transmission lines in general are a big topic but I'll refine it a bit and throw in a healthy dose of my own opinion. Straight lines are a mess, they will always have limited bandwidth, limited by a huge notch in response. A bit of taper in the line allows for almost ruler flat response and lots of bandwidth (if that's what you want), and stuffing helps too. I'm not a fan of El Pipo or any other straight tl.
As far as a zero construction build goes, from skimming your other thread I see your driver has come loose twice already. That's hardly ideal, and I can't think of any easy answer to that without at least a bit of construction.
If you can glue a driver to the end of a tube you can do construction. Home depot can make all your cuts and if you use plenty of construction adhesive (PL Premium) you don't even need angled cuts to form an angle, just fill the cracks with plenty of glue. The only cut you have to make yourself is the driver mounting hole, which I'm assuming you can do, otherwise your current project wouldn't be possible. And no matter how bad you might be, a belt sander and a coat of paint will make almost anything presentable.
As I show in the next post the "real world" performance is pretty good (?) especially considering the ease of making it. To date, the Sonotube TL is the only truly Carpentry-Free(TM) sub I am aware of 🙂
That looks a lot lot better than I was expecting, but like I said, move the mic a few inches and you will probably get something else. And if the driver isn't sealed well to the tube then you could get something else. The room is a powerful influence. If you really want to see how it performs take it outside (preferably in a wide open area) and measure it from a few different angles. An in room measurement will tell us what you hear at that exact spot in the room but it doesn't say anything about the sub's performance. Also, averaging 3 measurements is cheating if you moved the mic even a bit. (If you didn't move the mic they should all be the same.) And how much smoothing is used on these measurements?
I can't enlarge your screen shots very much for some reason. Request: would you send me the hornresp file you used? I think it's time I learn to use this program. I can model before I meddle. And in my spare time, read and write for Spanish Literature. Anybody have a tutorial for medieval or caribbean writings? 🙂
To enlarge screenshots, click on them and then click on the "expand" icon in the lower left corner on the image. You can use tb46's TH file, that will get you started, just import it into Hornresp. You will see that his sim is MUCH better than mine. His layout will require more than a simple single divider panel (more construction complexity) and it's a bit longer than mine. IMO it's still not the right driver though, this driver wants to be tuned lower than 20 hz in a tapped horn.
Sorry, I can't help with your foreign lit, but I can help with any questions you might have about simulations. Maybe you can convince your prof that Hornresp graphs ARE foreign language literature that you need to learn, and combine your passions that way.
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Proposed name change: "The Ijit Mark 1 Tampered Horn".
My frequency sweep of the Sonotube sub: Why is an average cheating? I averaged about 3 or 4 readings so that I could get a ballapark curve to program an EQ. Smoothing: none in that graph. I don't doubt your comments about the behavior of a QW tube. The frequency response will peak and dip from one place to another. Just like any other subwoofer in a typical room 🙂 The point is to have good sound about where you normally sit.
What makes a "30 hz tapered horn" (Cowan's) 30 Hz? I can't figure where the 30 Hz comes from. From the dimensions, the QW would be around 47 Hz. The Fs of his driver was 49 Hz. Is the 30 Hz the "half octave below Fs" rule-of-thumb?
If so, my Tampered Horn is 8' tall, so 1/4 wave = 35.3 Hz and half octave below that would be about 26 Hz.
My frequency sweep of the Sonotube sub: Why is an average cheating? I averaged about 3 or 4 readings so that I could get a ballapark curve to program an EQ. Smoothing: none in that graph. I don't doubt your comments about the behavior of a QW tube. The frequency response will peak and dip from one place to another. Just like any other subwoofer in a typical room 🙂 The point is to have good sound about where you normally sit.
What makes a "30 hz tapered horn" (Cowan's) 30 Hz? I can't figure where the 30 Hz comes from. From the dimensions, the QW would be around 47 Hz. The Fs of his driver was 49 Hz. Is the 30 Hz the "half octave below Fs" rule-of-thumb?
If so, my Tampered Horn is 8' tall, so 1/4 wave = 35.3 Hz and half octave below that would be about 26 Hz.
My frequency sweep of the Sonotube sub: Why is an average cheating?
It's perfectly fine for what you are using it for (if you do it right and get a good representation of your room's response, which is probably unlikely with only 3 measurements) but it's useless to anyone that wants to know the actual response of the sub. If you want to know the actual response of the sub, measuring it in-room is bad enough, measuring it in-room and averaging a bunch of measurements makes it completely useless.
What makes a "30 hz tapered horn" (Cowan's) 30 Hz? I can't figure where the 30 Hz comes from. From the dimensions, the QW would be around 47 Hz. The Fs of his driver was 49 Hz. Is the 30 Hz the "half octave below Fs" rule-of-thumb?
If so, my Tampered Horn is 8' tall, so 1/4 wave = 35.3 Hz and half octave below that would be about 26 Hz.
I assume he called it "30 hz tapped horn" based on his observation of it's tuning and/or it's low frequency knee. I doubt it had anything to do with the line length.
Once you start introducing any kind of taper into the line, the tuning vs length can't be predicted by 1/4 wavelengths anymore.
A tapped horn isn't a horn, it's a transmission line with clever driver placement to avoid the need for stuffing to achieve flat response within the desired bandwidth. Here's a very good resource for transmission line design - http://www.quarter-wave.com/TLs/Alignment_Tables.pdf
Ignore the math if you like, but read as much of this paper as you can. The parts that relate to line length vs tuning frequency are the chart on page 10 and Attachment C, starting on page 32. After reading those two sections you will see that taper has as much to do with tuning as line length.
So you have a couple of options if you want these answers. Either start reading up on theory (mainly tl theory, mixed with a bit of horn theory) or start simulating.
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Is the 30 Hz the "half octave below Fs" rule-of-thumb?
I forgot to address this part. The "half octave below fs" rule of thumb is just a suggestion that works fairly well. For sure you want fs to be above your desired tuning but it doesn't need to be exactly half octave above. In certain situations you can break this "rule" completely and still get good (but not ideal) results.
In post #8, bwank explained exactly why you want fs to be higher than your desired tuning frequency. The theory doesn't matter much though unless you have a couple of years to read and study the how and why of tl and horn design. Just take the rule of thumb at face value and start simulating, using drivers with fs up to a full octave higher than your desired tuning frequency.
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