Big BenD Bass Horn: Belts and Braces part 2
[Previous: Belts and Braces, part 1; Main; Next: The Mouth Bend]
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.
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Big BenD Bass Horn: Belts and Braces part 1
[Previous: Rear chamber and Middle Section; Main; Next: Belts and Braces, part 2]
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.
 Tappan, Peter W.: "Loudspeaker Enclosure Walls"; JAES Volume 10 Issue 3 pp. 224-231; July 1962
 Iverson, James K.: "The Theory of Loudspeaker Cabinet Resonances"; JAES Volume 21 Issue 3 pp. 177-180; April 1973
Big BenD Bass Horn: Rear chamber and Middle Section
[Previous: Throat Bend; Main; Next: Belts and Braces, part 1]
The Middle Section (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.
Big BenD Bass Horn: Throat Bend
[Previous: Scale Model; Main; Next: Rear chamber and Middle Section]
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".
Big BenD Bass Horn: Scale Model
[Previous: Design; Main; Next: The throat bend]
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.