Old School Horn vs Modern Vented Box

The 12Pi Hornresp sim does not show a saddle, but as built it does, with the average measured frequency response fairly close to the sim.

Lilmike's sims shows more of a saddle than as built, and comes in 5 Hz higher (1/3 octave!) than the sim (within 1Hz of the driver's FS).

So which is more accurately built 🙄?

Again, I don't know anything about the 12Pi so I can't comment on it.

Lilmike's F20 sim shows the LF knee starting to turn downwards at about 22 hz. The measurement shows it starting to drop at about 24 hz. That's not a 5 hz difference. I wouldn't say it's negligible but it's certainly not a big deal. Anyway, that's not what this discussion is about.

It's about the saddle right above tuning, and the GROSSLY undersized F20 clearly shows that the saddle does not need to be a problem.
 
True, but the secondary train of thought here (one of the secondary trains of thought) is the cause of the saddle in the Labhorn, that's been my only contribution here.

WRT the original topic I agree completely with weltersys' evaluation from post 32.

As far as any debate over horn vs vented box, the vented box wins by a bit from an output per transport size standpoint, but TH or FLH win from an output per driver and watt.

Considering the horn option can cut the amount of drivers in half, and power by 1/4, from a cost standpoint when transport is not figured in, horns are a big win.

If we are going to continue going off on a tangent about Lilmike's F20 sim (my sim) vs measurement (his measurement), all I can say is that it's a pretty impressive match considering the fact that simulators are a 1d prediction that take VERY few details into account. I don't know the details of his measurement conditions or equipment, I don't know if it was built perfectly (or even properly, I don't think he even built it himself) I don't even know if he measured the driver to make sure the t/s parameters were accurate or if he just used published t/s. Regardless, the sim vs measurement is more accurate than most when it comes to big horns.

The Labhorn original design sim vs measurement isn't very close at all. It's VERY impressive considering that it was done without any simulation or CAD but it does have a big saddle that shouldn't be (or at least doesn't need to be) there. And when power compression starts that saddle just gets worse. I think I showed pretty clearly WHY it's there.
 
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Just a guy, with your tone I was tempted not to reply at all, now that I think about it, it’s pretty weird you would get bent out of shape reverse engineering a design that is 14 years old and done without Akabak and McBean’s simulator and transferred by sketch twice into cad drawing by two others.

It, like the earlier Servodrive’s did in fact go against the horn wisdom of the day or at least that of manufacturers back then in using a compression ratio and suitable heavy strong drivers. Speaking of which what I gave was a target to shoot for and Eminence was the only loudspeaker company to follow through and make a suitable driver for the group, get the picture, you couldn’t have even made one back then.

Also speaking of targets, are you modeling a group of 6 like they asked for? Do you design at 1W or have you really looked at the response when the qe is increased from “power”?
Lastly like I also said, horn are resonant devices, when the there isn’t sufficient / proper resistance at each end, the resonances become unmasked , that’s why the pattern is roughly the same for all.

If you think you have done better using modern design tools while staying within the constraints the group picked, lay out what you can actually fit in the box, build it measure it and submit it to psw. There haven’t been that many people willing to design projects for free, let alone ones that beat what you could buy in the day or last as a viable live sub like the lab sub has. Conversation over.

Art, yes I think that’s right about max output with some boundaries;
Limited to system which have realizable driver parameters (that’s what the Servodrives had back in the way old days, an alignment that was happy with a 3.3:1 compression ratio). Here one also finds that making a vented box with a tuning much below Fs, becomes very difficult while the mass reacting on the cone in a tapped horn optimally uses a driver with an Fs above to well above the low corner.
Limited to direct radiators within the “magic” quarter wavelength circle, beyond which mutual coupling goes away and they radiate independently. This is why we don’t see many arrays of direct radiators for high power at high frequencies.
Conversely, direct radiators are the cost intensive, weight intensive, power intensive solution and a large enough array of subs also produces an “extended” impulse train due to differing path lengths like line arrays made of direct radiators. There are some adventurous folks in Germany that have been doing EDM stuff without our speakers and are going to use several groups of 2X2 of TH415’s and J-3’s for some big EDM thing in May. What they normally use are dozens and dozens (like 80 I think he said) of vented boxes so we will see how the difference comes across.
 
Art, yes I think that’s right about max output with some boundaries;

Limited to direct radiators within the “magic” quarter wavelength circle, beyond which mutual coupling goes away and they radiate independently. This is why we don’t see many arrays of direct radiators for high power at high frequencies.
Conversely, direct radiators are the cost intensive, weight intensive, power intensive solution and a large enough array of subs also produces an “extended” impulse train due to differing path lengths like line arrays made of direct radiators.
Tom,

Being liberally conservative, I prefer to do "more with less" and share your enthusiasm for horns.

The problem of disjointed independent radiation of direct radiators (or large horn arrays) can be addressed by making the array like a tunnel (or parallel walls of transducers or mouth exits) and applying progressive delay to the individual elements at 1/4 wavelength intervals (just under a meter for a 100 Hz crossover), basically an "end fire cannon".

As well as giving a coherent LF point source, the "end fire cannon" can offer a huge reduction in rear radiated energy while eliminating the extended impulse train due to differing path lengths, as the progressive delay makes the exit a virtual point source.

Funny, back when I compared your Servodrive BT7 to my similar sized BR back in the late 1980's, the cost of time aligning the rest of the PA (x 4 four way systems, a dozen delays = $12,000+) put them out of contention, but now DSP processing makes things affordable and viable that were just pipe dreams back then.

Unfortunately, even the thought of being in front of a single source radiating 150+dB now makes me cringe, though it is far more easy to accomplish than in the "old school horn" days.

Art
 
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Within the boundaries of the OPs "vented box example" we are looking at about 131 db continous output out of the single PK box, with an f3 around 34hz. Power compression is likely not *very* high considering there is still a considerable amount of xmax left in the tank with the manufacturer specified 30hz hipass (12 mm of excursion in passband at 48ish hz, 10mm at 28hz) and power available from their chosen amp (although tracks like "hunter" and other lower than 3 crest factor tracks centered around 35 hz will likely cause power compression). The center port is not *too huge* at approximately 700 square cm, but it appears to keep vent velocity under 18 m/s even when pushed to 2000 watts per box, providing a bit of evidence for minimal port compression at max power.

the danley TH118, which has the same nominal impedance (4 ohms), is actually a bit smaller (42x28x22.5 vs 45x30.5x22.5), has similar sensitivity (actually a bit higher), and will take the same 90 volts at 4ohms that the pk sound sub is given via its onboard amp, with a slightly lower hipass (which is offset by the tapped horns faster decline below tuning). all of Excursion is higher (as per the sims) so one may argue there may be slightly more distortion, but it may be negligble. In the end this adds up to very similar continuous spl and extension, with the Danley box using half the number of drivers but pumping twice the watts to it (being as its a 4 ohm driver, each box still only uses 2000 watts).

Id expect similar performance (with a bit more oomph above 45) from the keystone as well (which is still smaller than the pk sound sub).
 
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Just a guy, with your tone I was tempted not to reply at all, now that I think about it, it’s pretty weird you would get bent out of shape reverse engineering a design that is 14 years old and done without Akabak and McBean’s simulator and transferred by sketch twice into cad drawing by two others.

Maybe I wan't clear enough, although I thought I was. The first time I saw the Labhorn I was very impressed and I still am several years later. This sub is a big part of the reason I started learning about horns and it's still the design that is on my mind more than any other. I have a huge amount of respect for this design, and for the guy that created it. As far as I'm concerned, you are the only person that has made any significant advancements in the audio field in the last 50 years or so. While materials and drivers have improved, the only significant advancements in audio science concepts (like the Unity, Synergy and tapped horn) have come from you.

Having said that, the Labhorn isn't perfect. Most people still think it is, it seems like I'm the ONLY one that has ever reverse engineered it. The original design (before folding) was close to perfect (probably as close as you can get in an imperfect world) but the plans do not reflect the original design.

I was just trying to point out that the Labhorn is not perfect, and why it is not perfect. That's what we do here, reverse engineer to find pros and cons of any given design and hopefully use that info to improve our own designs.

It, like the earlier Servodrive’s did in fact go against the horn wisdom of the day or at least that of manufacturers back then in using a compression ratio and suitable heavy strong drivers. Speaking of which what I gave was a target to shoot for and Eminence was the only loudspeaker company to follow through and make a suitable driver for the group, get the picture, you couldn’t have even made one back then.

I was not on the scene 14 years ago, I have no idea what the horn wisdom of the day was and I don't know what drivers were available. What I do know is that the AES Leach horn paper is dated 1979 and Akabak has been available for 20 years now.

From what I can tell (since I don't have ALL your design posts) the Labhorn original unfolded design is a beautiful implementation of Leach's math. But the folded design (as per the plans) have a couple of problems that can mostly be solved with a simple refold.

As far as the use of Akabak goes, I was under the impression that you used it to design the Labhorn, although Akabak is never specifically mentioned. There are several paragraphs in your design notes that talk about your computer predictions of response, amplitude of ripple, efficiency, etc. I'm not sure how you predict any of that without Akabak, and from the description of the flat response it sounds like it was simulated as end loaded, not offset. You also mentioned a few times tht you made changes based on the computer predictions. Here's a couple examples but there are a lot more in the notes:

Here is what the computer
says, someone will have to back this up with real measurements before we can
say this is what it really does (predicted).

For a group of 6 units on the ground, the response is flat from about 31 HZ to
about 80 Hz. At the low end, the -3 dB point is about 27 Hz, -6 at 25 Hz and
-10 dB at about 21 Hz. Above 80 Hz, a slow roll off begins, ending at -3 dB at
about 150 Hz, -6@ 200 Hz.
The efficiency in the 30-80 Hz range (6 boxes 1/2 space) averages 55% and for
4 boxes the average efficiency is about 45%. I will be sending plots of all
this stuff as soon as I get it organized.

I had a
chance to run the models for the subwoofer using fewer units. I will scan
these and send them to Dave shortly but I will describe them now as they are
cool..

I assume you have looked at the predictions for 12 units flown, 6 units ground
stacked so I will refer to those. Also, for all cases, I adjusted the drive
level to the point of reaching X-max, going beyond which produces much more
distortion.

8 units flown / 4 units ground stacked
SPL is 146-146.5 dB, ripples are very small, about 1/4 dB peak to peak.
-3@ 28 Hz, -3@ 140 Hz
80 Hz and below, efficiency is about 42%.

6 units flown / 3 units ground stacked
SPL is 143-145 dB, ripples are about 2 dB peak to peak (+ - 1 dB)
-3@29Hz, -3@ 125 Hz
90 Hz and below, efficiency is about 32%

4 units flown / 2 units ground stacked (1 unit on the ground, against a wall)
SPL is 139-146 dB, ripples are about 3.5 dB peak to peak
-3@29 Hz, -3@110Hz
90 Hz and below, efficiency is about 20-25%

2 units flown / 1 on the ground
SPL is 132-143 dB, ripples are about 7 dB peak to peak
Large peaks at 31, 53 and 85 Hz
-3@29, -3@100Hz

The efficiency bounces from a few % to peaks of 40%, averaging about 10-15%

Moving on ...

Also speaking of targets, are you modeling a group of 6 like they asked for? Do you design at 1W or have you really looked at the response when the qe is increased from “power”?
Lastly like I also said, horn are resonant devices, when the there isn’t sufficient / proper resistance at each end, the resonances become unmasked , that’s why the pattern is roughly the same for all.

If you think you have done better using modern design tools while staying within the constraints the group picked, lay out what you can actually fit in the box, build it measure it and submit it to psw. There haven’t been that many people willing to design projects for free, let alone ones that beat what you could buy in the day or last as a viable live sub like the lab sub has. Conversation over.

I design in groups of 1, 2, 4, 8 and 12. Yes, I raise qe to see the effect of power.

Like I said, on paper it's easy enough to raise the flare T to get more output in the same volume and with the same drivers. But, like I said, those paper gains might not pan out in real life due to the stress of the higher compression ratio and higher power compression.
 
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1)Having said that, the Labhorn isn't perfect. Most people still think it is, it seems like I'm the ONLY one that has ever reverse engineered it.
2)From what I can tell (since I don't have ALL your design posts) the Labhorn original unfolded design is a beautiful implementation of Leach's math. But the folded design (as per the plans) have a couple of problems that can mostly be solved with a simple refold.
3) But, like I said, those paper gains might not pan out in real life due to the stress of the higher compression ratio and higher power compression.
1)There are no "perfect" cabinets for all uses.
Plenty of people have reverse engineered the Labhorn, but few have bothered to measure it. In the last 14 years, I never have seen a measurement of six or more.
The measurements that were at one time posted, (Michigan Sub Shootout 2002, Silas Pradetto's 1,2 and 4 Labhorn tests) no longer seem to be available, do you have some reputable measurements of Labhorns, or are you just basing your comments on simulations?
2)Build your "simple refold", and test it under same conditions as the Labhorn, and post both results so we can determine if you have "perfected" a design using a good horn driver from around 14 years ago that is not a real contender (thermally) anymore, though still remains a good value for displacement /dollar.
3) Since you say the paper gains may be ephemeral, the only way to prove them is by building and comparing.
Try it and show us how well it works.
Remember to build to build six 45" x 45" x22.5"cabinets, the size and quantity for the LabHorn design.
Hope you have plenty of space!

Art
 
Remember to build to build six 45" x 45" x22.5"cabinets, the size and quantity for the LabHorn design.

Why would that be required? Surely he only has to build one to see if it matches the sim for one.

Me, I'd like to see a "baby Lab" design, you know something based around a smaller driver and a smaller box, with similar FR (I'll accept the lower efficiency). Should make it a bit easier to transport 🙂
 
Why would that be required? Surely he only has to build one to see if it matches the sim for one.

Me, I'd like to see a "baby Lab" design, you know something based around a smaller driver and a smaller box, with similar FR (I'll accept the lower efficiency). Should make it a bit easier to transport 🙂
A FLH design that results in flat response for 1 sub will not be flat when 6 are used, the LF dip that JAG sees as a problem in one goes away in multiples as the combined mouth area gets to the design goal realized by 6 horns.

If you get flat response out of a small FLH having the low corner as a Labhorn (around 35 Hz), you will also find it is not as efficient as a vented box of similar exterior size.

Been there, done that- if you want small and low, BR and TH are the way to go, but once you get to Labhorn size and above, things start to even out more.

FLH designs using the large portion of the cabinet for the mouth like DSL's boundary horns (currently BC412 and BC 415) interest me more than a 45" deep horn, I cut down all my 45" deep FLH cabinets to 30" back in the mid 1980s so they would work in theaters, 45" was too deep to go in front of the fire curtains in most.

After lopping off 33% of the cabinet, the "V" loaded BR had way more LF than the (short) horn.

Art
 
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I'd like to point out that only one of the amps in the cx800 could likely power a stack of at least 6 to 8 series wired labhorns to xmax.... (90 volts into series wired boxes), providing the same output and extension as about 6 pk sound cabs (granted they take up 33 percent more space).

We know that PK sound used to deploy lab subs. We also know they claimed to start producing a subwoofer based on the design characteristics of the labsub , the cs212s (using "custom designed" drivers, and different chamber topology/horn charactaristics in a 45x45x22.5 space).

Eventually they moved on to their current dual18 vented enclosure. be it because of size/design conflict/driver failure rate/ ease of construction/performance , etc, we likely will never know.
 
1)There are no "perfect" cabinets for all uses.

Of course not. Once again, I'm only suggesting that the Labhorn has a big notch right above tuning tht doesn't need to be there. The cause of the notch is the fold. If the notch were to be fixed the Labhorn would be "perfect". (Not perfect for all uses but as good as it can be given the preset goals and limitations.)

Plenty of people have reverse engineered the Labhorn, but few have bothered to measure it. In the last 14 years, I never have seen a measurement of six or more.
The measurements that were at one time posted, (Michigan Sub Shootout 2002, Silas Pradetto's 1,2 and 4 Labhorn tests) no longer seem to be available, do you have some reputable measurements of Labhorns, or are you just basing your comments on simulations?

Measurements are hard to come by but there's one on PSW. The shape of the curve does look a lot like the sim I posted in post 27 (the last graph, light grey response). This shouldn't be much of a surprise though (even though my sim is not completely accurate - the dimensions are estimated and there's not enough segments in Hornresp to fully capture it, the biggest problem is that it's offset too far. And BTW, the sim is shown in .5 pi space which is the same thing as a stack of 4, which accounts for the rising response in the measurement that's not reflected in the sim). If you build what you simulated, the measured response will be very close to the simulated response.

An externally hosted image should be here but it was not working when we last tested it.


An externally hosted image should be here but it was not working when we last tested it.


If you are suggesting the saddle goes away in a stack of 6, it doesn't. It gets filled in a bit but not much.

2)Build your "simple refold", and test it under same conditions as the Labhorn, and post both results so we can determine if you have "perfected" a design using a good horn driver from around 14 years ago that is not a real contender (thermally) anymore, though still remains a good value for displacement /dollar.

Half the problem can be fixed by simply making the rear chamber 10 liters larger, as per the original (unfolded) design (5 liters per chamber). The flare is large enough that it can easily lose 10 liters without much change. I would hope that much at least is not in dispute.

As far as changing the flare itself to account for the offset driver, I haven't ever tried that and it would probably require a bit of redesign and a refold. All I'm suggesting here is that it isn't a good idea to simulate an end loaded horn but fold it as an offset driver horn. This should be obvious. Everyone was simulating as end loaded but folding as offset back then but that doesn't mean it was the right thing to do. Akabak was available.

3) Since you say the paper gains may be ephemeral, the only way to prove them is by building and comparing.
Try it and show us how well it works.
Remember to build to build six 45" x 45" x22.5"cabinets, the size and quantity for the LabHorn design.
Hope you have plenty of space!

Art

Tom specifically asked how much better one could do with modern design tools and CAD. I gave an honest answer, a couple of db on paper but maybe zero db in real life.

I've said several times now that the Labhorn original design (before folding) was an excellent design. But the plans (folded design) do not accurately reflect the original design. This is a fact. Even as it stands it's still a lot better than a lot of modern designs but it's not perfect, it has a big saddle that doesn't need to be there.

I'm kind of surprised at the resistance. I identified the saddle (actually the OP did but incorrectly explained it's cause), I correctly explained why it's there (in detail with supporting quotes and pictures) and explained how to avoid it. Why is everyone getting so upset?
 
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Once again, I'm only suggesting that the Labhorn has a big notch right above tuning tht doesn't need to be there. The cause of the notch is the fold. If the notch were to be fixed the Labhorn would be "perfect".

Measurements are hard to come by but there's one on PSW. The shape of the curve does look a lot like the sim I posted in post 27 (the last graph, light grey response).
An externally hosted image should be here but it was not working when we last tested it.


An externally hosted image should be here but it was not working when we last tested it.


If you are suggesting the saddle goes away in a stack of 6, it doesn't. It gets filled in a bit but not much.

I identified the saddle (actually the OP did but incorrectly explained it's cause), I correctly explained why it's there (in detail with supporting quotes and pictures) and explained how to avoid it. Why is everyone getting so upset?
The measured 45 Hz "big notch" is -2 dB on the "Danley 1.8v1m grnd", the upper response peak around 90 Hz +8 dB from 35 Hz.
You suggest the saddle "gets filled in a bit" "but doesn't go away in a stack of 6", but only show response of a single cabinet 🙄.

Your "20% undersized rear chamber" simulation shows approximately the same dip as the "Danley 1.8v1m grnd", but underestimates the 100 Hz peak by 6 dB, and shows a dip at 250 Hz, an octave off from the measured dip near 500 Hz:no:.

Your "full size rear chamber" shows approximately the same loss at 35 Hz as gained at 45Hz.

In 2007 Wayne P. "solved" the same response dip of his "12pi" with the "12pi V2" with front and rear chamber corrections in Hornresp, but has not shown a chart confirming any measured difference, the 2007 sub shootout shows the same response as the 2005 and 2006, which look nearly identical (but smoother due to the larger mouth and cabinet) to the Labhorn.
I suspect the correction did not amount to much or he would have included an actual measurement in his "history and development" which extensively documents his "improved" design based on the original Labhorn.

You propose no actual plans to accomplish a net wash in output, a simulation that does not conform to the measured cabinet, a proposal with a change on paper but maybe zero db in real life, no plans on how to do it, and wonder why we are not singing praises 🙄?

Art
 
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Me, I'd like to see a "baby Lab" design, you know something based around a smaller driver and a smaller box, with similar FR (I'll accept the lower efficiency). Should make it a bit easier to transport 🙂

Hey just a guy, why don't you accept Mr. Steele's challenge and design the "baby Lab." You seem to have a good understanding of the LabHorn's design, and you know your way around all the modern software and design tools that are available now.

Either stick with the Lab 12 driver and see how much you can shrink the cab - while still staying close to the original response, or just choose another driver and try to make something half the LabHorn's size that performs similarly.

You have stirred up a bit of tension here, and infuriating Mr. Danley (the God of Hornology) is not good for your karma. You have an audience here that has a high level of expertise, and I believe they would be VERY HAPPY to critique your design for you.

(HaHaHa - that is my evil laugh, I have a feeling these guys are going to come down on your design with their sledge hammer swinging).

It would be a great learning experience for you, and it is a golden opportunity for you to show them what you are capable of. The fact that someone like Mr. Danley actually drops by a forum like this and makes serious comments is unreal. To have him critique one of your designs would be an unbelievable opportunity for you. And the rest of the guys here are some serious deep thinkers with a remarkable level of knowledge. What they have taught me in the last month is mind blowing. Here's you chance just a guy, show us the best front loaded horn you've got.
 
I know some of you dont like mr. BFM, but heres his published charts for his "T45" (a little bit bigger than 1/2 a lab sub when built at 22.5 inch wide).

Lab12.gif
 
The measured 45 Hz "big notch" is -2 dB on the "Danley 1.8v1m grnd", the upper response peak around 90 Hz +8 dB from 35 Hz.
You suggest the saddle "gets filled in a bit" "but doesn't go away in a stack of 6", but only show response of a single cabinet 🙄.

Your "20% undersized rear chamber" simulation shows approximately the same dip as the "Danley 1.8v1m grnd", but underestimates the 100 Hz peak by 6 dB, and shows a dip at 250 Hz, an octave off from the measured dip near 500 Hz:no:.

Your "full size rear chamber" shows approximately the same loss at 35 Hz as gained at 45Hz.

This was all already answered.

... And BTW, the sim is shown in .5 pi space which is the same thing as a stack of 4, which accounts for the rising response in the measurement that's not reflected in the sim).

It was shown as a stack of 4, that's why the 6 db peak is "underestimated", as I already pointed out in the post you are attacking. The dip caused by offset at 250 hz in my sim is because it's offset too far due to not having enough segments in Hornresp to fully capture it. This was also explained in the post you are attacking.

The "loss" at 35 hz in my sim isn't a problem, the notch at 45 hz is the problem.

By putting "big notch" in quotes I guess you mean it isn't a problem. It gets worse when the power gets turned up and compression sets in.

You propose no actual plans to accomplish a net wash in output, a simulation that does not conform to the measured cabinet, a proposal with a change on paper but maybe zero db in real life, no plans on how to do it, and wonder why we are not singing praises 🙄?

Art

I don't want your praise but I do want you to actually read what I posted. Everything in this post has already been answered.

The simulation conforms quite well to the measurement when you take into account that it's a quick and dirty sim of 4 cabs and an offset of 32 cm. If I could have offset it less the dip caused by the offset would have been right where it was supposed to be.

Why am I responsible for submitted a better design? All I'm doing is pointing out the cause of the saddle and how to avoid it. And as I've said probably a dozen times already, the original design was close to perfect, until it was folded.
 
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Hey just a guy, why don't you accept Mr. Steele's challenge and design the "baby Lab." You seem to have a good understanding of the LabHorn's design, and you know your way around all the modern software and design tools that are available now.

Either stick with the Lab 12 driver and see how much you can shrink the cab - while still staying close to the original response, or just choose another driver and try to make something half the LabHorn's size that performs similarly.

You have stirred up a bit of tension here, and infuriating Mr. Danley (the God of Hornology) is not good for your karma. You have an audience here that has a high level of expertise, and I believe they would be VERY HAPPY to critique your design for you.

(HaHaHa - that is my evil laugh, I have a feeling these guys are going to come down on your design with their sledge hammer swinging).

It would be a great learning experience for you, and it is a golden opportunity for you to show them what you are capable of. The fact that someone like Mr. Danley actually drops by a forum like this and makes serious comments is unreal. To have him critique one of your designs would be an unbelievable opportunity for you. And the rest of the guys here are some serious deep thinkers with a remarkable level of knowledge. What they have taught me in the last month is mind blowing. Here's you chance just a guy, show us the best front loaded horn you've got.

It's actually much easier to design a stack of front loaded horns than to design a single horn. Everything you need is in Leach's horn paper. And since this info is incorporated into Hornresp you can design an ideal reactance annulled stack of horns in about 30 seconds with the system design tool.

Folding that design is a bit trickier since it's very difficult to actually fold an end loaded design, most of the time it's a lot easier to offset the driver. But that will lead to a saddle just like the Labhorn has unless you change the sim to reflect the offset driver.

I have no idea why this has become a "design something better" challenge. You can't do much better than Leach's math. But what you can do is accurately build what you simulated, or when that's impossible you can change this sim to reflect something that can be built.
 
I have no idea why this has become a "design something better" challenge.
Because you seem to think your changes in Hornresp inputs constitute a "design", while having demonstrated no certain way to improve the actual cabinet design, then defend your simulation as if it actually demonstrated an improvement.

Reducing output at the impedance and excursion minima, while increasing output at the upper excursion maxima does not translate to less heat in a Lab 12 when power is turned up and the coil heats up.
Even if a re-designed cabinet conforming to your simulation did happen to do what you think it would (which based on observations of measured cabinets of this horn geometry, probably won't), it may not be a net improvement.