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.

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William Neile Horns

In the previous article I already presented some basic information about the semi cubic parabola (Neile parabola) and why I got interested in this mathematical function (Link1). The initial intention was indeed to calculate curved fins with equal path lengths (arc length). But first, a verification of this mathematical function for it’s use as a horn profile should show acceptable results because the two outer Neile parabolas define the outer horn contour. Within most of my previous horn calculators two different functions in two orthogonal planes were sufficient to generate a point cloud by blending the two functions together to form an ellipse at each iteration step along the horn axis. But I decided against this procedure because in the meantime I could make some experiences how to generate a point cloud for radial like horns which can quite easily be made out of wood with a CNC milling machine. The reader should be familiar with the basic blueprint of a radial horn. For the use of the Neile parabola to this type of horns some things are a little bit different as we have no exact radial expansion from a pre-defined point of origin of the profile. In this article I will describe the basic steps how to create a William Neile horn and show some initial BEM simulations as proof of concept for this type of horns.

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A Tribute to William Neile

For some time now I have been investigating for the so-called fin horns. And for over a year now I have been able to generate complete point clouds for such horns. I myself own a replica of the TAD TH4001 horn and I think these horns sound very good and load the driver perfectly down to the lowest octave of the usable range of the driver. A passive crossover can therefore be implemented without significant problems.

What has always surprised or bothered me about these fin horns is the straight construction of the fins, which start on a section of a circle near the throat. My understanding is that a point sound source at the intersection of the two side walls is assumed. But what if the arriving wave front is not curved like the fin start circular arrangement? And what is happening in the small “pre-chamber” before the fins? My initial idea for a new approach was to use a mathematical function that starts directly at throat and which is curved and an analytical expression of the functions arc length is known. The resulting fins should start at throat, they should be be curved and they should end at the same path length along the curved trajectory. At this time I came across with a function discovered already in the 17th century that is named after William Neile (Link1) as Neile parabola. Another well known name is semi cubical parabola (Link2). It was the first algebraic curve to have its arc length computed (Link3). The semi cubic parabola bears an interesting property that it is an isochronous curve of Leibnitz (Link4) . All in all a very attractive looking function and worth to try it as a horn function. This article deals with my way to use the Neile parabola as horn function.

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