Big BenD Bass Horn: Design

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 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 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. 

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. 

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