The horn, especially the spire and mouth sections, have large flat panels, and these must be braced. Panel vibrations will act like notch filters in parallel to the horn path, and will suck energy from the sound transmitted through the horn. And not just that, the panel resonances may have high Q values, re-radiating the absorbed vibrations at the wrong time, with ringing. We clearly don't want any of this, but it may be hard to elimiate.
There are two papers that cover the basics of enclosure bracing: Loudspeaker Enclosure Walls by Peter W. Tappan  and The Theory of Loudspeaker Cabinet Resonances by James K. Iverson . These papers give both theoretical and experimental data on the effectiveness of wall construction and bracing, and should be studied by anyone making speaker enclosures.
Both wall absorption and resonant frequencies affect how much the wall will vibrate. Absorption is more effective the higher the resonant frequency, so raising the resonant frequencies is effective in several ways. Below the first resonant frequency (mode), it is the stiffness of the wall that limits vibrations, higher up the mass dominates.
If the first wall resonance could be moved out of the passband of the horn, this would massively reduce the contribution from the horn walls. Increasing the wall stiffnes can be done by using thicker material, adding tension, changing the shape, or bracing. The material is already 18mm birch ply and relatively stiff, and the whole structure could easily become difficult to handle if it was made thicker. The shape is given by the horn, and can't be changed (but it is possible to increase the tension in the panels by adding a slight curvature). Bracing is the most suitable approach, and tension is also automatically added in the curved section of the horn.
The most effective bracing method is braces along the long direction of a panel. Tappan recommends to place the braces so that the circles that can be inscribed in the unbraced parts of the panels are as small as possible. It is also important that the braces add enough stiffness to make a difference. If the brace isn't stiff enough, it will just add a bit of mass to the wall and may actually lower the resonant frequency.
At high frequencies the wall radiation is very directional, and for most enclousures this means that the parasittic radiation is directed away from the listening area and can be more readily absorbed. But in this horn, the front of the spire, although partially covered by the midrange horn, is a large radiating surface pointing towards the listening area. It is therefore critical to reduce radiation from this wall.
Comparing Bracing Methods
Usually one would put braces internally and externally on the horn based on experience, gut feel and what "looks right". But this may result in a lot of unnecessary braces, adding weight, and unneccessary work. Below are data for a 12" by 18" (305 by 457mm) steel panel, 0.02" (0.63mm) thick, clamped at the edges, and braced in different ways .
It is clear that the quite common perpendicular brace is not very effective in raising the resonance frequency, and that the perhaps less intuitive lengthwise brace is the most effective.
My first thoughts about reducing panel vibrations was to drive the horn with a signal generator and feel around for areas of excessive vibrations. My second thought was that maybe a knuckle test using the spectrum analyzer in Arta together with a measuring microphone could provide some more useful data, and allow me to move resonances out of the passband. Then I remembered I had an ACH-01 accelerometer. I built a phantom powered preamp for it, allowing me to use a normal sound card with microphone input. Then I could make repeatable, quantifiable measurements of bracing performance.
The first measurements were done on a rear chamber, throat bend and middle section (spire).
The rear chamber is a square box of about 65 liters. There is no bracing apart from a frame with T-nuts to bolt on the rear cover.
The panels will be left unbraced until the end. The back wall provides a reference measurement to check that the system is run at the same levels throughout the tests.
The throat bend has a lot of built-in stiffness from the bending. The main vibrations seem to be above about 800Hz, so there doesn't appear to be a great need for extra bracing here.
The next article will cover the bracing of the spire.
I actually started building the spire before the throat bend. It is a fairly straightforward
The spire is about 1m long and consists of nearly-parallel sides (the angle is just a few degrees). One of the narrow sides is straight, the other has two break points to approximate the exponential area expansion. I used the router on the throat end to make the walls where the flange connects vertical, so that the hole in the flange could be cut out easily.
This is all there is to say about the middle section for now, but I will return to it in the next part, since it needs quite a bit of bracing.
The rear chamber
The rear chamber is just a simple rectangular box. The sides have the same length, and although this sounds like something you shouldn't do, (square rooms have the strongest modes), there is a very good reason for it: The sides are the largest dimensions of the box, and therefore sets the lowest modes inside it. If the depth is kept, and the box is made to have an aspect ratio different from one, that will push the lowest mode lower. So to keep the modes as far away from the working range as possible, I decided to make the box square.
I also routed out space for the driver to move, both for 15" and 12" drivers. The box was made large enough to work with Altec 515-8G, 65 litres, as it is easier to reduce the volume than to increase it.
The front baffle has a rectangular hole that fits the horn throat, and 8 T-nuts to bolt it to the horn.
The rear cover also has T-nuts.
There is at this point no bracing inside the box, this will come later, based on vibration measurements.
Here are a couple of pictures of the first parts set up for the initial tests.
One way to test aspects of horn design which are hard to simulate, is to make a scale model and measure it under similar conditions. A friend with a small CNC machine cut some plywood sheets based on exported on-the-flat profiles of a simplified version of the horn, having only the mouth bend. The scale is 1:5.
The mouth bend is the most important in this case, as this sets the footprint of the horn, and therefore enables us to position the horn in the same way as it will be positioned in the room.
To drive the horn, a scaled down driver is also required. I used a Celestion AN2775 driver, as I had some at hand.
The horn was then placed in a corner, and a few experiments were tried.
Below are frequency response curves for the horn alone in the corner, and with a cardboard baffle flush with the horn mouth. There is a 5dB loss of sensitivity, similar to the simulated loss, so we may assume we will get a similar loss for the big horn in real life.
I also tried making a Helmholtz resonator under the horn, but this only reduced the loss by 1dB.
One of the first things I started building was the throat bend. Basically because it was a fairly small part, that was easy to build before the garage got filled up by the large mouth bend and mouth sections. But as you will see in the background on some of the pictures, some of the other sections were also under way during the building of the bends.
In laying out the bend, I had first drawn everything up in CAD. At the centre of the arc I drew lines every 15 degrees, and measured the inner and outer radii. On the plywood I similarly used ruler and compass to divide the circle into 15 degree segments, and used the dimensions from CAD to draw up the outer curve. The aluminium ruler was (ab)used as a spline ruler to get a smooth curve.
With the curves drawn, the four side walls were cut and sanded to match each other. As mentioned previously, I decided to go for constant width most of the way around this bend.
For the part nearest the throat, I changed the profile from constant width in order to make the throat more square. Using a router table, I got the angles right so that everything matched up without gaps.
The throat bend is built on a sheet that serves as a flange for both ends: one end connects to the spire/middle section, the other end to driver box. This stabilises things and puts less stress on the bend itself.
The throat end and the bend sides are connected using wooden dowels.
The sides are then glued to the flange, also using wooden dowels for support. These are drilled and hammered in from the outside, leaving the inner surface untouched.
For the inner curve, three layers of 5mm bendable plywood were used. The curve was too steep to use other types of plywood without steaming.
The inner surfaces are then painted to reduce absorption.
The "ceiling"/outer wall has an innner skinn of aluminiumm. A groove is routed in the side walls.
Laminating the outer sides was a bit tricky. I Used two layers of 3mm hardwood plywood and 2 layers of 5mm bendable plywood. Getting things properly aligned took some practice, and I found it was easiest to nail each layer using small nails, instead of using clamps.
A view from the bottom, showing the aluminium "ceiling".
I have wanted a bass horn ever since I moved from Øyfjell. In Trondheim I had to make due with an Altec 816A enclosure, which has a horn, but that's more of an upper bass/lower midrange horn that doesn't add much to the actual bass. Moving to England I didn't even have the Altecs, and the first house didn't have enough space to set up much more than the midrange horns with open baffles. The open baffles, using either Altec 515-8G or various drivers I built, had decent performance, which is probably one reason why I kept them for so long. Another reason is I didn't have time to work on a big horn while writing the Book. But I was of course thinking about various options.
I could easily fit a horn mouth of 70 by 100cm, this would take up similar space to my baffles. Using a J-folded horn with the driver near the ceiling, I could easily get about a 250cm horn length, and with a throat area of 300cm2 the horn cutoff would be about 35Hz. With an Altec 515-8G the response is quite smooth, if the horn is placed in the corner:
The throat impedance is also quite smooth:
This is for the horn placed in a corner, i.e. eighth space. In practice, however, the horn will be out on the floor, since I live in a rented house and can't make horn-sized holes in the walls. We'll see the disasterous effects of this shortly.
There are many ways to fold and bend horns, as outlined in the Horn Book, chapter 26. Sharp folds cause powerful reflections, and typically the throat resistance falls to zero save for at the resonances, above a few hundred hertz. Gentle bends with a bend severity parameter (ratio of horn radius or half width to the bend radius) smaller than unity, on the other hand, have much less reflections, and less issues with loss of radiation resistance and peaks and dips in the response.
In order to make it easier to play around with the geometry, I rewrote the horn curving tool in my simulation software, so that bends could be specified in several ways. For variable radius bends, this included some math in order to find the length around the bend. I also wanted to be able to specify two out of three of the parameters bend length, bend radius (relative or absolute) and bend angle. For the one-dimensional simulations I had also implemented the 1D theory outlined in the Horn Theory chapter in the book. While an approximation, it would at least give an indication of the change in acoustic length at low frequencies.
As mentioned, I was also considering building a midbass horn, but with the effect of the rear wall causing a loss of radiation resistance right above the corner frequency of the horn looked like it could be troublesome. So after some thought, I decided to build a bass horn based on the initial ideas.
In the meantime I had also looked into designing a dedicated bass horn driver. Many of the classic bass horn drivers, like Altec 515 and JBL 2220 are 15" drivers, and building something similar was of course an option. But there are some factors that suggest this is not optimum for domestic use. A domestic bass horn does not need the power capacity of cinema and PA speakers. Even a couple acoustic watts is plenty, easily producing 120dB SPL in a small room. With the high efficiency of bass horns (25-50%) there is very little demand on the driver. I am all for having plenty of headroom everywhere in the system, so that amplifiers and speakers are only coasting along at even the highest peaks. But even with my open baffles, with C-weighted average SPL of 112dB in the listening position, the peak instantaneous power to the woofers was in the order of 30W. The bass horns should be at least 10dB more efficient.
Therefore a 12" driver would be a better choice. Cone breakup would also be pushed higher, and considering I wanted this horn to behave nice way above the intended 300Hz crossover frequency, that sounded like a good idea. Diaphragm displacement could still be kept low.
A 12" driver has a piston area of about 550cm2. I would like to keep the compression ratio low, so I selected a throat area of 250cm2. With an RE of 6.5ohms, a Bl of about 18Tm would be suitable. Diaphragm mass should be fairly light, and the suspension soft, in order to use a relatively small rear chamber. While I didn't have such a driver at hand, I planned to build one.
The geometry went through several iterations. With the smaller throat area I had to make the horn longer. After some number crunching I also found that I could get a bit more deep bass out of it if I made it slightly longer, placing the cutoff at 30Hz. This became the base design. The mouth was kept at 7000cm2, 1m wide and 70cm tall.
The first part of the bending geometry to be worked out was the mouth bend. Making a bend often involves laminating thin plywood, or using bendable types. Or both. I therefore looked into having a constant width bend to simplify things: this way simple flat plywood side walls could be used. But this geometry has quite sharp discontinuities, and it's also not visually satisfying.
I therefore went for a simply curved bend. This means that the side walls also twist around the bend, necessiating a somewhat complex jig for laminating. But there is no longer any sharp discontinuities. I also decided to use a constant instead of variable curve radius, together with a vertically asymmetric geometry. The inner curve is therefore quite close to a constant radius too.
The mouth segment was designed to be fairly flat on the top, to provide a "shelf" for the midrange horn. This also set the depth of from the horn mouth to the front of the upright part, so to make it possible to fit the length of the midrange horn there.
The middle segment, which I call the spire since it goes straight up, is asymmetric. This is to push the horn into the corner, so it doesn't cover too much of the window.
The throat bend was designed last, and here I chose to use a constant width for most of the length. Initially I considered a 90 degree bend here too, but since this would place quite a strain on the joints from the lever action and the weight of the driver, I made it a 180 degree bend in the end.
At this point I basically had the geometry laid out. See 3D rendring below.
There is space below the horn, the reason for that will become clear soon.
The horn was first simulated using a 1D model, with the horn mouth flush mounted in a corner. This is the infinite baffle + two reflecting surfaces boundary condition. It is easy to calculate the radiation impedance and SPL under these conditions. Here is the SPL response at 1m on-axis:
In the listening postion the response is not as extended, both due to directivity and interference from the floor and side wall reflections.
The throat impedance also looks pretty good:
Under these conditions, I also made an FEA simulation of the horn, to look at the wave fronts inside. Using gmsh for meshing, and Pafec for simulations, the geometry was exported, meshed ans simulated. Symmetry planes were used to create a corner boundary condition.
The geometry was simulated before I had settled on the 180 degree throat bend, but the rest of the geometry matches the final design. The wave fronts heave well inside the frequency range I intend to use the horn (up to 300Hz). At 460Hz we start to see mode formation in the mouth bend, and the wave fronts are somewhat rough even at 355Hz near the mouth. This is to be expected. Adding a lumped parameter driver model to the horn, we get the on- and off-axis results shown below (2m distance). There are no great peaks or dips in the working range.
But the horn will not be flush mounted in a wall. The mouth will be about 1.25m in front of the rear wall. The SPL in this case is shown below. There is about 5dB loss in bhe low frequencies due to the rear wall reflection.
The reason can be seen in the throat impedance, which is much more peaky compared to the flush mounted condition:
And the reason for this is the effect of the rear wall reflection on the radition impedance.
There isn't really any practical way around this. Possible solutions would be
Knock a hole in the wall and flush mount the horn
Make the horn mouth a lot bigger
Move the bend nearer the mouth
Build a baffle in the room, effectively making a partition
None of these are very practical for me. In addition comes the complication of room modes, which I will return to later. However, there is an option that could be worth investigating: making the reflection weaker, for instance by using a Helmholtz resonator near the rear wall, under the horn (this was the reason for the space underneath the horn). I will investigate this using a scale model. Possibly an active solution could help too. But regardless of this, an impedance matched driver will give the smoothest possible response in any situation, so this must be implemented.