The mouth bend has larger surfaces that most of the other parts so far. They are curved, which does add some stiffness, but they are still large.
The outer bend is the largest surface, and still resonates quite a bit despite the tension from curving.
With all measurements in a single plot, it's quite difficult to make out the individual curves. But it is clear that there is quite a bit of vibration from 200Hz and up, and also a few resonances around 80Hz which are probably the bell mode.
If we take a look at point 33, which is in the middle, 600mm along the curve from the throat end, we find clear peaks at 240Hz and 340Hz, with smaller peaks nearby. By adding a brace across the width of the horn 250mm from the mouth end, brace n, the lowest of these are reduced substantially, while those around 300-400Hz remain. Adding braces along the horn reduces the 240Hz modes by 5dB more, but does not help much above 300Hz.
At point 35, which is at the center, 900mm from the throat, we find other modes. The cross brace now reduce the modes up to 400Hz at this point.
Two bends along the horn, near the middle, also reduce the vibration quite a bit.
The two braces along the horn near the edges actually increase the vibration a bit, but they are required for the stand, so they have to stay.
I also experimented with a sash clamp across the mouth. Across the width of the mouth it cleaned up the 90-180Hz range a bit, across the height it cleans up the 180-300Hz range.
the side panels mainly have modes in the 200-500Hz range.
I added two braces to the side. The first was vertical (with the horn in the upright position), and reduced the vibration at position 36 by about 5dB.
Adding a horizontl brace added another 5-10dB. Since I actually braced the side before the outer bend, I also include a measurement with the mouth bracing added, this also helped reduce the side vibration somewhat. Below 250Hz the level is now about 20dB from where it started.
The inner bend already has some braces, and the siginficant resonances are above 200Hz.
Some additional braces were added in between the original braces, but this was done rather late in the process. Here is a measurement of the inner bend with the mouth section added. This reduced the vibration enough to be insignificant compared to the vibration from other panels.
The final bracing of the mouth bend is shown below, as is the two measurement positions 33 and 35 used for checking the mouth bend.
The third part of the horn air path is the mouth bend. This is the most complex part of the build, because all four sides of the bend are curved. In addition, the sides twist as they go around the bend. The best way to go about this is to do a similar approach to what we did for the midrange horn: laminating several layers of plywood on a jig.
Then bend is 90 degrees,and the end surfaces are well defined. The inner bend radius is constant, but the outer radius varies. Additionally comes the twisted side walls.
As a start, I set up two boards at right angles. To these boards, two other boards were fixed, these serve to hold the inner dimensions of the horn.
Two arms will hold spacers for shaping the side walls. These are fixed to the main jig with T-nuts.
Here the side wall spacers are in place. They are important since the side wall twists as it goes around the bend.
The flanges are used as part of the jig, to help push the plywood towards the inner panels.
The inner bend is made from bendable plywood. The bracing is fixed to the flanges (the little rectangular 3mm plywood piece is used as a guide for the wooden dowel in each brace), and then works as the jig for the bend.
Three layers of bendable plywood are laminated to make the inner wall.
The sides are cut using a jig. The jig is a piece of plywood marked from an "on-the-flat" drawing of the side panel. The on-the-flat dimensions are calculated from the computer model by a series of vector rotations etc. These pieces (cut a little oversize, as it's hard to get perfect accuracy) are laminated on the jig, and clamped tight against the jig spacers.
Here you can see how the side walls twist around the bend. The same phenomenon can be seen in the Western Electric horns, and is very clearly visible in the 12A horn.
The outer wall is made from a combination of 3mm hardwood plywood (inner and outer layers) and bendable plywood. I found it easiest to fix the layers with small nails as I put them on, rather than using clamps. Pieces of plywood are used to hold the layers in place against the flanges.
Or not really. The final thouches will of course be bracing, sanding and painting. But when laminating this many layers, and also pushing them against a flat surface while at the same time trying to align them correctly, put on clamps etc, it's hard to get a clean edge at the flanges. To improve this, I used the router to remove 3mm of the inner, outer and side walls, and fill these spaces with strips of 3mm plywood. This removes all the unevenness between the layers, and creates a flat, smooth surface for the flange.
The finished bend (except for bracing) looks like this.
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.
As shown in the previous part, the wall vibrations in the throat bend are essentially out of band, thanks to the dimensions of the bend being rather small. Not so in the middle section (spire), though. Here the main culprit will of course be the front and back, but let's start looking at the sides first.
In the figures below, the curve legends correspond to the file names. The numbers refer to the measurement position, and the letter after the number refer to the bracing that has been applied. A list is given at the end of this article.
I measured the vibrations at the straight side wall in three places along the centre line: 200mm and 500mm from the top, and 200mm from the bottom.
Similar with the curved side wall, here I also measured along the centre line, but at the centre of the three straight panels that make up the curve.
There are some strong resonances in these panels, and both have strong peaks at around 125Hz. There are also troublesome peaks at about 200Hz and 300Hz too, these are in, or too close to the working range (up to about 300Hz) to leave them alone.
The first thing I did was to add a flange to the mouth end of the spire. This is quite effective in moving the lowest (125Hz) mode, which is a bell mode. For the sides, I added braces along the length of the horn, this also reduced the vibration significantly. Most of the vibration is now moved above 200hz, and the leve is reduced by about 10dB.
Here is a compraison between braced and unbraced panels for the straight sidewall:
And here are the curves for the three measurement positions along the curved side wall, after bracing:
This part is quite important, as it will face the listener. Unbraced, the responses at 7 different positions at the front wall look like this:
There are some very strong modes inside the working range, and we need to kill those. For the following curves, I will only use measurement position 22, which is 800mm from the top (about 200mm from the mouth), and about 290mm from the straight side wall.
Adding a brace close to point 22, running all the way along the front from top to bottom, in addition to the flange (unfortunately I don't have measurements of the effect of the flange alone at point 22), reduces the level below 300Hz a bit. There seems to be several modes located around 180Hz.
It is clear that for bracing to be really effective, the brace needs to be significantly stiffer than the panel it braces. For the braces applied so far, I used 18mm birch ply on end, about 50mm wide strips (apart from the brace for the curved side wall). While it helps, plywood has limited stiffness. I therefore tried adding a 40x40mm L angle iron, 4mm thick, to the D brace. This cleaned up the range above 200Hz significantly, but didn't suppress the 180Hz modes much.
Adding a second brace from top to bottom improved the vibration above 200Hz further.
Finally I added corresponding braces on the back, a small brace on the front near the mouth on the curved side, and a small brace near the throat of the spire. This introduced some modes aroudn 700 and 1000Hz, which may come from the coupling between back and front.
In any case, the bracing has improved the wall vibrations a lot, what is left is the big bump around 180Hz, which is probably the bell mode shifted higher due to the mouth flange.
Below is a photo of the applied bracing. The braces are labelled according to the legend.
Next up will be the construction and bracing of the mouth bend.
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.