Big BenD Bass Horn: Belts and Braces - Appendix

This appendix will show measurement of the unbraced wall and final performance of the braced wall with everything in place. It will contain one figure for each measurement point, with a few exceptions, divided into sections for each part. 

Rear Chamber

The bracing was applied at the end, after all other bracing, as the measurement at the back of the rear chamber was used as a level reference to keep all measurements comparable. 

Throat Bend

Not much was done here, so I suspect the reason for the difference in vibration comes from the way the horn parts were supported during the first measurements, compared to when the horn is upright. 

Spire/Middle Section 

The main objective here was to push the modes above the passband, and it does seem to have been fairly successful. 

Mouth Bend (Inner)

Mouth Bend (Outer)

Mouth Bend (Side)

Mouth Top

Mouth Bottom

The measurements do not show much improvement over the "unbraced" condition. That is most likely because the bottom panel was braced from the start; the braces were used as a jig for the curved panel. But a few additional braces were added (RA), although they don't seem to have improved things. This may be due to the ground not being completely flat when these measurements were made. The WH measurements were made inside the garage, with the horn firmly placed on a flat concrete floor. It also seems that some vibrations were transferred from other panels, possibly through the cross brace, as some additional modes appear in the WH case, compared to R (unbraced mouth).

Mouth Side

Here the lower bell mode(s) have been considerably reduced, especially by the addition of the extra side brace that turned the mouth side edges into 'C' beams. 

 Cross Brace

Positions 61 and 63 are the right and left sides of the horizontal brace, 62 is the top part of the vertical brace, and 64 is the bottom part. 

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. 

Bracing Basics

There are two papers that cover the basics of enclosure bracing: Loudspeaker Enclosure Wallsby Peter W. Tappan [1] and The Theory of Loudspeaker Cabinet Resonances by James K. Iverson [2]. 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 [1].

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. 

Measurements

 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. 

Initial Measurements

The first measurements were done on a rear chamber, throat bend and middle section (spire). 

Rear Chamber

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. 

Throat Bend

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. 

[Previous: Rear chamber and Middle Section; Main; Next: Belts and Braces, part 2]

References

[1] Tappan, Peter W.: "Loudspeaker Enclosure Walls"; JAES Volume 10 Issue 3 pp. 224-231; July 1962

[2] Iverson, James K.: "The Theory of Loudspeaker Cabinet Resonances"; JAES Volume 21 Issue 3 pp. 177-180; April 1973

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. 

Side Walls

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:

Front Panel

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.

[Previous: Belts and Braces, part 1; Main; Next: The Mouth Bend] 

Legends

Big BenD Bass Horn: Belts and Braces part 3

[Previous: Belts and Braces, part 2; Main; Next: The Mouth Section]

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.

Outer Bend

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. 

Side Panels

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. 

Inner Bend

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.

Final Bracing

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. 

[Previous: Belts and Braces, part 2; Main; Next: The Mouth Section]

Legends

Big BenD Bass Horn: Belts and Braces Part 4

[Previous: Mouth Section; Main; Next: Performance Measurements] 

In this final article on bracing, we will look at the mouth section braces, and also compare the measurements of the final horn with some of the original, unbraced measurements. This article will be quite long, as there is a lot of ground to cover, and many experiments. As before, I can't show all the measurements, as there is just too much data too look at. But I will include measurements at strategic positions, which I used to evaluate the performance during application. 

At the bottom of the article is a photo of the braces with letters to identify them (the letter R indicates the mouth without bracing). These letters correspond with the letters in the curve legends. 

The bottom wall was fairly well braced from the start, as the braces were used as a jig. But additional braces were added later. We will take a look at the bottom wall when looking at the final results. 

Mouth Side Wall

 The first set of measurements show the vibration at the unbraced side wall at all the measurement positions. While quite messy, we see some strong modes at 112, 185 and 350Hz, the lowest is the bell mode of the mouth and is very hard to get completely rid of. 

 Adding the centre horizontal brace on the side wall, S, shifts the bell mode down somewhat, and cleans up another weaker mode around 58Hz. The range above the bell mode is also cleaner, but the upper modes are not much affected. Adding the T braces (upper and lower horizontal braces) helps in the range above 300Hz. 

 A vertical side brace, U, does not do much with the bell mode by itself, but it cleans up the upper modes. 

 At this stage I was starting to think I may have to apply some more drastic measures to the mouth to kill the bell mode. So I got some more angle iron, and applied around the mouth. Below are the measurements of these reinforcements by themselves, V indicates side angle iron only, W indicates side and top angle iron. It's actually not much of an improvement by itself, apart from at the 58Hz mode. Well, at least that indicates that something is right...

 Some slight changes by adding the vertical side brace:

 We'll revisit the side when more bracing is in place. 

Mouth Top

 Without bracing, two things are clear: The absolute level of the peaks is lower (for the most part) than for the side, and the actual bell mode is the mode at 58Hz. 

Adding the angle iron (W) reduces the bell mode by 5dB, and adding the front lateral brace (WB) reduces it by another 5dB. But these braces do not do much for the rest of the modes. 

Adding a rear lateral brace (WC) and two longitudinal braces (WD) helps somewhat, adding another four longitudinal braces helps even more. 

Mouth Cross Brace

There was no way around it: The mouth needed a cross brace. A cross brace is of course very efficient in killing the bell mode, but it's not as good for killing the other higher modes of the panels. So both are needed. Adding the cross brace certainly reduces the panel vibration over a wide range, the bell mode is now down by 25dB, and the rest of the range up to 300Hz is much cleaner. Adding Mutestrip between the two braces, where they intersect, doesn't do much, but I left it there since very little of the material is used anyway. 

But of course the mouth braces themselves will vibrate too! The horizontal brace has two distinct peaks at 67 and 70 Hz and a strong one around 300Hz, while the vertical brace has several peaks above 300Hz. 

 In order to combat the resonances of the horizontal brace, which were the most troublesome since they were quite strong in-band, I tried various things like stiffening with steel L-profiles. But the most efficient turned out to be mass loading the arms of the horizontal brace with pieces of flat steel. The result of this is shown below, it took the level of the peaks down by over 10dB. 

The braces added to the outside so far are shown in the photo below:

Order of Application

When braces are glued onto the side walls, it's not easy to experiment with the order of application. But since I'm building two horns, I decided to test out the order of application at the mouth section. 

Side Walls

For the first horn, here are a couple of measurements with no bracing (R), all outer braces (WF) and finally outer braces pluss cross brace (WH).

If the cross brace is added first (includes also the rim braces, I haven't measured without those), there isn't actually too much of a difference when the outer braces are added. 

But what really killed the vibration, especially the lower modes (at this position) was the addition of a second layer of bracing at the mouth, that can be seen at the photo below. This was an idea suggested by my friend Torbjørn at the very end of the experiment, so it is not included in the previous mouth bracing experiments. It basically turns the rim braces and horn walls into 'C' beams.

Mouth Top

For the top wall, similar tests were done. Again, R is with no bracing, WF is with all outer braces, and WH is all braces including cross brace. 

RA indicates the rim braces and cross brace, but now the outer braces (RD) makes some difference, especially around 100-200Hz. 

Conclusion

The measurement of the efficiency of the bracing has been quite extensive. Over 300 measurements have been saved, but probably the same number have been taken in the process of testing things, finding good measurement points, and so on. The articles have presented only a select few of these. For those interested in a summary of "before" and "after" measurements for all measurement points, curves wiht a few comments are presented here.

For the most part, the bracing has been successful. Vibration has been reduced by at least 10dB most places, and in many cases a lot more. Several places the modes have been pushed out of band, other places they have been usefully attenuated. In a few cases, coupling has introduced vibrations in surfaces that weren't there to begin with. 

Bracing and vibration are definitely complex topics, and this study has taught me a lot about practical bracing. The main points:

• The braces must be stiffer than the panel it is meant to brace, and considerably so. Otherwise they will just add mass and lower the resonance frequency. 
• Raising the resonance frequency by partitioning the panel works, if the braces are stiff enough. 
• The bell mode is hard to kill by external bracing, and typically need cross bracing, although turning the rim braces into 'C' beams helps considerably. 
• Cross bracing can transmit vibration from one panel to another, and excite vibrations in the panels that were quiet. They are not perfect solutions and should be used with care. 
• The larger the panels, the more difficult it seemed to raise the mode frequencies by bracing. My initial goal of moving all modes out of band were not met for the larger parts of the horn, probably for a large part because the braces weren't stiff enough. 

But all in all, the horn is a lot deader than in its unbraced state, and although it's hard to quantify the amount of vibration contributed by the horn walls, I think it's probably not much compared to the direct radiation from the horn mouth, as there are no definite dips or peaks in the response that could come from spurious resonances or vibration.

Appendix

[Previous: Mouth Section; Main; Next: Performance Measurements] 

Big BenD Bass Horn: Design

[Previous: My Approach to Bass Horn Design; Main; Next: Scale Model]

 The requirements for the bass horn was set up in the overview article, and some additional considerations are outlined in My Approach to Bass Horn Design. This article will outline the basic design of the Big BenD horn.

Initial Idea

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. 

Horn Bends

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. 

New Design

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 R_E 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. 

Geometry

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. 

Simulations

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 gmshfor meshing, and Pafecfor 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. 

Rear Wall

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

1. Knock a hole in the wall and flush mount the horn
2. Make the horn mouth a lot bigger
3. Move the bend nearer the mouth
4. 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. 

[Previous: My Approach to Bass Horn Design; Main; Next: Scale Model]

Big BenD Bass Horn: Installation

[Previous: Performance Measurements; Main; Driver Update] 

Finally, the last article about the Big BendD bass horn! This part will cover the installation and setup of the horn, with some comments on the subjective performance at the end.

Installation

Although the DIY 12" driver showed the most promise during outdoor testing, I still wanted to try the Altec 515-8G when setting up the horn. It was mounted in the rear chamber, the chamber was filled with wool, and the rear wall covered with pieces of an acoustic celing tile. 

Then came the process of carrying all the parts into the living room, setting it up, adding gaskets, bolting it all together, installing the drivers, wiring it up and put the rest of the system back together. In the process I had help from my good friend Harry. This is really a two-person job, because carrying the big parts into the house isn't easy to do by oneself. The parts were all designed to fit through a standard door, but they are still a bit difficult to move around. 

With two people working, the setup was done in a couple of hours. There are a lot of bolts, about 70 per horn, so or ratchet spanners got a real workout. 

The complete setup is shown below. The white middle/throat sections blend in with the walls, making the bass horn less dominating in the room. It does work, some people have not recognised it as part of the bass horns.

The First Test: Where's the Bass?

Just setting up the horn and putting some music on, without any crossover or EQ, left us wondering: Where's the bass? Isn't this supposed to be a bass horn? There's a lot of lower midrange, but the sound was a bit thin. 

The measurements made it obvious what the problem was: the output fell below 70Hz, and apart from a peak at 50Hz, the response was more like a midbass horn than a 30Hz bass horn. What was going on? 

We swapped the Altec for the DIY 12", and that helped significantly; the better impedance match between the horn and driver was definitely an issue in the presence of room modes. Which turned out to be the real problem.

Room Modes

 My living room is about 7m long and 3.5-4m wide. This means that the second mode in the length direction and the first mode in the width direction are both at about 50Hz, which is also clear from the measurement above. Between these two modes, energy transfer in the room is quite limited. A wider room would definitely be an improvement, but you have to work with what you've got. 

In the modal region in a room, the response can vary quite a lot from position to position. Some listening positions have a smoother response, while others place the listener at peaks or nulls of modes. To find the best starting point for EQing the response, I measured the response in the room at a 2.5 by 3m grid, every 0.5m. The results for all positions are shown below. 

It turned out that the response was quite smooth about 3m from the horns mouths, somewhat behind the middle of the room. The responses at this line are shown below. Annoyingly, the response drops quite sharply below 45Hz, due to the lack of modes between 25Hz and 50Hz, but apart from rebuilding the room (which I'm sure the landlord wouldn't like), there's not much to be done. 

I have applied some EQ to lift the response a bit, but one should be very careful with EQing dips caused by room modes. And I'm not going to spend the rest of my life in this house, so hopefully my nest home will have a more beneficial distribution of modes int eh listening room!

Listening Tests

So, after all this work, how does it sound? The lack of output below 45Hz is only noticable on music where you know there should be something down there. Apart from that, the response in the listening position is quite smooth, and it has the traits of bass horns that I have been missing for so long: proper impact - even at low volumes -, and responsive, detailed and tight bass. Low frequency details in the recordings are quite easy to hear, and there's no overhang or resonance. It sounds effortless even at very high volumes too. The horn integrates well with the fast and detailed midrange of the Axi2050, making it a good combination. I also tried a delay-derived subtractive crossover, as described in the Horn Book, and it made a worthwile improvement to the coherence and naturalness in the lower midrange.

All in all, I'm very satisfied with the performance. 

[Previous: Performance Measurements; Main; Driver Update] 

Big BenD Bass Horn: Mouth Section

[Previous: Belts and Braces, part 3; Main; Next: Belts and Braces, part 4]

The final (and largest) part of the horn is the mouth section with its bracing. The mouth section was designed to consist of mainly straight panels, with only the lower panel being curved. 

Since the mouth section is quite big, I figured the best way to build it was by using the bracing and flanges as a jig. Below is the lower flange and the support for the rear of the mouth section. The two are spaced apart according to the design, and held in place temporarily by a couple of scrap pieces. 

Then the lower braces are put in place and screwed to the throat flange and the lower mouth flange.

The extra support can now be removed, and the first layer of the lower wall can be fixed to the braces by nails and glue.

Two more layers of 6mm plywood are laminated onto the first.

Note the routed slit in the lower mouth flange. This is to make a proper and good looking termination for the laminated lower panel. By doing this carefully, there is no gap between the panel and the flange. 

Side and top panels in place. Since the side panels flare outward, they have to be cut in a way that makes the top and bottom panels flush with the cut. See the Midrange Horn for one way to do it using a band saw. For this horn, I made a small jig to tilt the jig saw the right amount (equal to the angle of the side walls) when doing the cuts. 

Side braces and a top brace are added and fixed using wooden dowels. 

With the mouth section done, a support frame for the mouth bend was made. It is bolted to the outer braces of the mouth bend. 

And finally the horn can be assembled. Here is the first mock-up without using any bolts. The next stage now is to add braces to the mouth section, and the acoustic performance of the horn can be checked.

[Previous: Belts and Braces, part 3; Main; Next: Belts and Braces, part 4]

Big BenD Bass Horn: Performance Measurements

[Previous: Belts and braces pt. 4; Main; Next: Installation] 

 With one horn finished, I took it outside to do some frequency response measurements. First thing to do is to measure the horn under conditions similar conditions to the simulations. This is a very important part of designing speakers, if you want to use simulation tools in the process. You need to verify that your simulation is correct, and if not, in what way. It is especially important if you are writing your own simulation software. I think people are getting better at it, but there have been many cases on DIYaudio of people complaining about their simulations being wrong, when the actual problem is that they have not simulated what they have actually built. 

Corner

The actual condition of a horn built into an "infinite corner" (3 infinite baffles perpendicular to each other) isn't easy to achieve in practice. The best I could do was to use the walls of my house and garage:

And then put some extra sheets of plywood between the buildings to try to close the gap.

So, finally the first measurements, with and without baffles. The difference isn't huge, This may be because the garage is still close enough in terms of wavelengths to contribute to the baffle effect. (I'm not sure if the levels are actually correct, trying to do the calibration in ARTA gave some confusing results.)

So how well does this fit with the simulations? Actually pretty good, see below. The Response below 200Hz is almost spot on, the  response at higher frequencies deviates, probably because of the simple model used for simulating the curving, and because I used a different driver than in the measurements. 

What I'm quite happy with is that the curving approach worked as intended: there are no sharp dips and peaks or suckouts in the response, and it doesn't roll off until about 500Hz. This creates a nice overlap with the midrange horn. At the lower end, the response starts to fall off rapidly below 30Hz, which was the intended lower limit. The response is a bit uneven, but we'll see that this changes with a different driver.

Wall

The second test condition is in front of a wall. Neither of the two are fully representative of the operation conditions in actual use, but it will show the effect of placing the horn in front of, instead of flush with, a wall.

The effect of one missing side wall and the increased distance to the back wall is evident: a loss of level at low frequencies that was predicted by both the simulations and scale model measurements. 

Driver Tests

The next measurements were done with REW as I found it easier to do a level calibration there than when using ARTA. Four different drivers were tested:

Altec 515-8G, a 15" driver built in a Celestion FTR-3070 chassis, A 12" guitar speaker, and a 12" high efficiency woofer built using various parts available. The results are shown below. 

There is a clear difference between the drivers; the guitar speaker clearly fails and has a very peaky response (not all musical instrument drivers are suitable for bass horn use, even if Dr. Bruce Edgar had good results with EVM-12). The 15" drivers perform about the same. The best results comes from the 12" driver I built. This isn't actually very surprising, since it has the best impedance match with the horn of all the drivers. 

The dips in the response at 483Hz and 870Hz are from standing waves in the empty rear chamber.

Distortion

Following is some distortion meausrements of the drivers tested. I measured at 95, 105 and 115dB SPL at a 2m distance. Only the results for 115dB (114dB for the 12" prototype) are shown.

The 15" drivers are quite similar in response, but the Altec clearly has lower distortion. The guitar driver has very high distortion (not surprisingly, since it has a stiff paper surround and only 1mm overhang on the voice coil), and is best left to what it was designed to do: create distortion for electric guitars. 

The 12" DIY driver has the smoothest response, and while the distortion is slightly higher than the Altec, they are both quite at "sane" listening levels.  

[Previous: Belts and braces pt. 4; Main; Next: Installation] 

 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.

[Previous: Throat Bend; Main; Next: Belts and Braces, part 1]

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. 

[Previous: Design; Main; Next: The throat bend]

Big BenD Bass Horn: The Mouth Bend

[Previous: Belts and Braces, part 2; Main; Next: Belts and Braces, part 3]

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.

The 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. 

Inner Bend

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. 

Sides

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.

Outer Wall

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.

Final Touches

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.

 [Previous: Belts and Braces, part 2; Main; Next: Belts and Braces, part 3]

The Big BenD Bass Horn

Those who have followed the evolution of my system, will have noticed that I haven't had proper bass horns since 2010, before I moved to Trondheim. In Trondheim I had Altec 816Abins, but they don't count as bass horns. They have a cutoff of about 160Hz, and create a bump at about 200Hz, which made them a bit challenging to cross over to my midrange horns. 

Proper bass horns is something different. Having experienced horn loaded bass down to some 35Hz before, I miss the physical impact, detail and texture you get with proper horns. So after the Horn Book was completed, and I had recovered from the experience and enjoyed some spare time (although most of it in lockdown), it was time to bring a bass horn into the Kolbrek household again. 

Having coauthored the book on horn speakers, I knew I couldn't take shortcuts. Like building someone else's design! There are many clever and experienced horn designers out there, but in addition to using the knowledge gained while researching the book, I also wanted to make a horn that would match my room and system. 

First Ideas

I started thinking about this several years ago. Some quick calculations showed that a 2.5m long horn with a 7000cm2 mouth, using an Altec 515-8G driver, would produce decent bass down to about 40-45Hz. It could also be built in the form of a J, with the mouth at the floor and the throat near the ceiling. But at this stage I was still workig on the book, and had neither the time nor the tools to start such a project. 

A second idea was to build a midbass horn covering down to about 100Hz, and making a subwoofer for the frequencies below 100Hz. The concept I was toying with was using two 12" drivers in a straight midbass horn, with about the same mouth size as the bass horn outlined above, and some sort of Slot Loaded Open Baffle (SLOB) built into a platform the horn could stand on. This would make the horn design fairly straightforward, but had the complication that I needed another amp and two more DSP channels. While I plan to upgrade my DSP, this approach required too many changes to the system to be convenient. Another problem was also showing up.

When the first lockdown started in 2020, with furloughs and working from home, I was asked to worked reduced hours. The extra time was spent extending my horn simulation software to approximate the reflections from a rear wall. Hornresp assume a corner horn to be placed in the actual corner, essentially the horn is built into one of the walls. In my PhD I extended this modelling to allow the horn to be moved away from the corner, but still being mounted in one of the walls. This does some rather unpleasant things to the radiation impedance, creating dips that create larger impedance ripple and reduced output. 

Using the image source method and a simple low frequency approximation for diffraction, I was able to model the horn in front of a rear wall in a way that matched reasonably well with BEM. All good so far. Except this placement had the same shortcomings as when a horn is moved away from the reflecting surfaces. The added time delay and phase shift creates dips in the radiation impedance and response. For the placement I had planned for the midbass horn, the dip came right at the lower end of the band, effectively pushing the lower 3dB frequency up by a significant amount. 

So after some simulation and thinking, I abandoned that idea too, and began looking at the J-curved horn again. And I realised that to make a horn like that, I had to upgrade my curving tool. That took a few months, but then I was ready to design my new bass horn.

Requirements

Before starting a project, it's good to make a list of requirements. Then work from the requirements towards a design that will fulfill them. In my case, I wanted the following:

• Bass down to at least 40-45Hz
• Not (too) undersized mouth
• Not critically dependent on driver parameters
• Easy to cross over to the midrange horn at about 300Hz
• Modular

Low Frequency Extension

The low frequency extension depends on the horn lenght and mouth size. Essentially we want the throat impedance of the horn to follow that of the infinite horn as closely as possible, but this is impractical for bass horns. We should still try to avoid impedance peaks. The lenght also needs to be sufficient, so that the first impedance peak isn't placed too high. This becomes more critical the smaller the mouth becomes. 

Not Undersized Mouth

This is important for to reduce the impedance ripple. A good match between driver and horn (set by driver parameters and throat area) will minimise response variations in the face of impedance variations, but the horn can often end up fairly narrowbanded, especially of it is folded. 

But mouth size is also set by practical limitations. In my case a mouth size of about 100 by 70 cm was the largest I could allow. This is a fairly substantial mouth size, nearly the size of the baffles I currently use, but still relatively small for a 40Hz horn. I would have to accept a compromise here. 

Driver Dependency

If throat impedance ripple is reduced, so is sensitivity to driver parameters. This means that several drivers are possible, and that I can experiment without having to do major modifications. 

Crossover

Crossovers in horn systems can be tricky. Direct radiators may have some bandwidth outside the crossover frequency, but are still often pushed quite far. Textbook crossovers require the response of the drivers to be flat way past the crossover frequency, otherwise the response of the drivers have to be factored in when designing the network. Or, if using an active crossover, EQ applied to flatten the response so that the acoustic slopes are as desired. For horns, things often seem to be pushed even further. Horns need to be a certain size to be usable down to a given frequency, and although they have high group delay near cutoff, people often want to use as much of that hard-earned bandwidth as possible. Bass horns are often extra tricky to cross over, as they may be folded and have response irregularities, sharp dips and peaks that makes the phase go haywire. 

I usually cross my midrange horns at around 300Hz, so the horn should behave well up to at least 400Hz, preferably higher. When testing horn folding methods for the Horn Book, I noticed that a fold typically creates a sharp loss of resistive loading above about 200Hz in typical bass horns. This would not be good for a wide band bass horn. 

Curving, on the other hand, while having its own challenges, doesn't create the reflections and cancellations of a folded horn. Therefore the horn would need to be gently curved, not too sharply. 

Modular Build

In order to get the horn into the house, it would have to be divided into sections. This also makes it possible to experiment with inserting other sections, removing sections and so on. It creates more possibilities for problems, like leakage, but the flanges also act as bracing. 

The "Blameless" Concept

In his articles, and later books, on power amplifier design, Douglas Self describes the concept of a "blameless amplifier". The concept is, in his own words,

"...the concept of what I have called a "Blameless Amplifier", the name being chosen to emphasise that the remarkably low THD comes from the avoidance of errors rather than from fundamental advances in circuitry."

I have a great deal of respect for Mr. Self and his approach to audio design, and especially the blameless concept is something well worth adopting for more than amplifiers. Oftentimes we want to make "the best" speaker or amplifier or turntable by applying some new and inventive concept, while very good results can be had by identifying problems in old and "boring" technology and fixing them. Self identified a series of distortion mechanisms in a classic, standard amplifier topology, and through simulations and practical tests reduced or eliminated these mechanisms. 

In the same way, I will try to eliminate or reduce as many problems as possible in this bass horn. Since it is my first design using this approach, and since the thought came up after I had started building the actual horn, it will not be completely blameless. But I will, as far as possible, do scientifically and rationally guided choices, backed up by simulations and measurements. 

The Horn

 Since this design will take some time to complete, I will post updates in my blog, using this article as an index page to the blog entries. 

1. My Approach to bass horn design
2. The design
3. Scale model
4. The throat bend
5. The middle section and rear chamber
6. Belts and braces pt. 1
7. Belts and braces pt. 2
8. The mouth bend
9. Belts and braces pt. 3
10. The mouth section
11. Belts and braces pt. 4
12. Performance measurements
13. Installation
14. Driver update

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".

[Previous: Scale Model; Main; Next: Rear chamber and Middle Section]