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.