Acoustic Loading Optimized William Neile Horns – Part 1

It is quite a long time ago since I wrote my last article about William Neile Horns. There was definitely considerable progress exploring and refining this new type of horns, but unfortunately the lack of spare time did not allow it to be documented. The attentive reader will certainly not have missed the fact that one of my fundamental goals is to achieve a good acoustic horn loading almost down to the desired cut-off, but the William Neil horns presented so far behave more or less like classic waveguides with regard to horn loading as there is no visible cut-off, instead of this a very slight roll off of the radiation impedance towards low frequencies happened. Although, some people might in fact prefer the loading properties of my first William Neile horns. 

This article series will deal with acoustic loading optimized (ALO) William Neile horns which means that acoustic loading should be pushed to the most reasonable level down to the desired cut-of frequency but at the same time keeping the resonances / reflections of a classical exponential wave front surface area expansion to a minimum. I am aware that there is a controversial view about horn loading in the community. Some say that horn loading is almost unimportant as you can simply push the driver where you need the output. Directivity control should be the major design objective of a horn . I have a different view on this issue as generally without proper horn loading you need to push the driver more and more towards lower frequencies where it hurts most as the excursion doubles with each octave towards lower frequencies and when there is any need to push the driver even more – it might work technically – the excursion needs are even larger, so this is never the best solution.  Horn loaded compression drivers are an ideal combination with low power single ended tube amplifiers using a passive crossover – well, usually there is almost no output power left to push anything. The speaker has to sound great with the first Watt of output power and even with much less. So with more low frequency loading from the horn you get more SPL in that region and less output power means less excursion for lower frequencies. My experience is that a compression driver used within the acoustic loading optimized frequency band of a horn (resistive loading) will give you much better micro dynamics with an open and effortless sound. What I intend with new ALO William Neile horns is to combine good acoustic loading characteristics and good directivity control especially for the horizontal plane. This is not an easy task but as we will see that it is possible.

The BEM simulations of the final ALO William Neile horn designs were indeed so promising that is is planned to have the first prototypes made since the inherit property of the Neile parabola obviously provides the capability to obtain very good directivity control especially with smooth transitions along the frequency pass band of the horn. This property combined with an exponential throat section and an appropriate mouth termination flare there is a valid prospect of an excellent horn design.

The usual approach to design an acoustic loading optimized horn is to start the horn profile with an exponential construction wave front surface area (cwfsfa) expansion. The cwfsfa expansion could be either exponential or hyperbolic with T in the usable range of about 0.6 to 1.0 and in fact trying different T values is a valid optimization strategy. The common approach for a horn that could be placed directly on top of a bass cabinet is to favour the horizontal plane of radiation and to adjust the vertical plane of radiation so that the overall result is an almost exponential or hyperbolic expansion of the underlying cwfsfa. This of course limits the options to influence the vertical directivity control as the vertical profile is constraint to fulfil the cwfsfa expansion up to certain point of the horn axis. Sometimes I tend to think that horn design is a certain kind of art, to get the appropriate sections of the horn optimally. My latest horn designs are therefore essentially divided into three different zones/sections. First there is the exponential zone with the basic horizontal opening arrangement, then the zone of control of the vertical radiation and then the flaring zone. The corresponding zone transition points can take place horizontally or vertically at different positions on the horn axis. I have programmed a quite complex spread sheet calculator for this task and you have to know exactly which parameters need to be changed for a distinct result. Therefore it is not planned to share this calculator.

Initial considerations about meaningful use cases for such horn designs focused on two different driver categories. First, many 1″ drivers have a suggested crossover point in the range of 1.2 kOhm. My general design objective is that the horn should be able to load approximately one octave lower than this, which defines a cut-off around 600 Hz as the first design constraint. This should provide most flexibility trying different crossover slopes. With steeper crossover slopes even crossover points considerable below 1.2k should be possible depending on the driver used. The directivity control of the horn should at least cover about 60 degrees for the horizontal plane and not less than 30 degrees for the vertical plane. Target frequency point for this goal is about 5k. Higher than 5k would even be better. The overall decay of the directivity control should look smooth and even as far as possible. To be avoided are constant solid angles in the horn profile as these produce only excellent directivity control in a limited range of the horns frequency pass band and end up with a knee-like behaviour at higher frequencies where the directivity control suddenly breaks down. The second use case should be a 1.4″ horn with much lower acoustical loading. This will be covered in part 2. Depending on this results a 2″ horn would be an option. Although, it should be mentioned that the lower the acoustic loading is targeted the harder it is to keep control about directivity as the overall horn length must become considerably longer and the initial opening angles are smaller for the exponential section which contradicts the capability for a broad radiation.

To summarize the basic blueprint of the ALO William Neile 1″ horn the profile starts of course with the round throat entry. This round throat is virtually divided up into four equal pieces which merge into the rounded corners of the horn. The horizontal cwf expansion is made quasi isophase as it is built from an infinitesimal number of evenly distributed Neile parabolas all with equal arc lengths. The vertical cwf is flat so that the overall cwfsfa is like a bended 2D piece of paper which greatly simplifies the math. This simplification is working well when the vertical profile is smaller than the horizontal which is given by the basic blueprint of the horn. I will show again a sketch of the algorithm:


William Neile Horn hrz and vrt Profile Expansion (round throat to rectangular with rounded edges)

William Neile Horizontal Construction Wavefront (quasi isophase)

The different sections / zones of the resulting horn profile as described above should be combined so that it is not immediately obvious where the boundaries are located. So there  should not occur any visible sharp knees. To make it short, this is the final optimized 2D profile:

Acoustic Loading Optimized William Neile 1″ Horn Profile

Although the underlying profile expansion principle is quite simple it provides a really smooth transition from a round throat to the quasi rectangular blueprint with rounded edges which should be obvious by looking at the 3D profile images:

But the ultimate question is how well does the new ALO William Neile horn is performing with respect to the design goals? Well, I usually use BEM simulations to answer this question with sufficient accuracy. The software used to do this job is again AKABAK for BEM and VACS for visualization. Thanks again to Mr. Joerg Panzer for supporting my work. Constant velocity drive is used for all presented results here.

Although I am able to do my own BEM simulations based on exported point clouds directly from my calculator, DonVK supported me to create a model with a roll-over using CAD software to reduce the edge artefacts of the BEM simulation. This should be a more realistic setup for a real world horn than using meshes with sharp edges or skinny angled meshes:

First of all, let us check how well the horn is loading down to the desired cut-off. I decided to show the impedance amplitude as the usual diagram with real and imaginary parts is often a source of misconceptions about the loading capabilities:

Radiation Amplitude Impedance

The corresponding simulated SPL in 1m, 2m, 3m distance is supporting that we can expect very good acoustic loading at least down to 600 Hz.

Predicted SPL (const. velocity) at 1m, 2m, 3m distance

It should be mentioned that a real world compression driver might show a much more linear SPL compared to this constant velocity results. Is is no miracle that horns can be optimized for very good loading but together with very good directivity control is a real design challenge. What should I say, from my personal opinion the radiation polar are excellent too with nearly 70×50 up to 5k which is much better than the initial goal:

WNL Horn Horizontal Radiation Polar (3dB step)

WNL Horn Vertical Radiation Polar (3dB step)

The overall behaviour is very smooth and also the decay is even and smooth.

WNL Horizontal Polar (0-90, 5 degrees step)

WNL Vertical Polar (0-90, 5 degrees step)

Finally, the directivity index DI90 of the new ALO William Neile 1″ horn. When all different sections of the horn harmonize perfectly together we can observe such a nice linear behaviour up to the highest octave without any visible break down of directivity control:

WNL Horizontal DI90

WNL Vertical DI90

I am really happy with the results and the combination of very good loading and very good directivity control is imo outstanding. Looking back to all of my previous designs I am absolutely convinced that this horn will be a very good performer without any ifs and buts and therefore I plan to have a prototype made.

DonVKs round-over version of my 1″ ALO William Neile Horn

I could already motivate a few people around the world to support me creating the first layouts for prototypes made of wood. Stay tuned how this project is going on!