Some time ago I presented the first article about my development of the ALO William Neile horn type and the underlying construction method. Although, most of my previous worksheets use a super ellipse for each 3D layer / spline along the horn axis. To have an alternative option for William Neile horns I have implemented the the necessary math together with evenly distributed Neile parabolas used in this context to build up the horizontal construction wave front. All William Neile (WN) horns based on the super ellipse algorithm will get the extension “SE” in their name.
By varying the Lamé exponent of the super ellipse formula many different shapes from elliptical to almost rectangular are possible. At throat everything always starts with a Lamé exponent of 2 which indicates an ideal ellipse. Of course, if major and minor axis of the ellipse are equal there will results a perfect circle at throat. If major and minor axis differ an ellipse will result. Generally, the major axis is the horizontal plane because it is intended to radiate more broad compared to the vertical plane (minor axis). For higher Lamé exponents of the super ellipse formula the resulting shape will be an almost rectangular spline but a transition function is needed to provide a smooth transition from exponent 2 to higher values along the horn axis. A very similar procedure was already used for my spherical wave horn (SWH) and JMLC worksheets.
This article is about the first making of such a horn by DonVK who much preferred the native elliptical shape and asked for my assistance to optimize a horn for his setup. Finally, we ended by with two horn of different cut-off. This article describes the making of the first smaller version.
But let me go first into more detail about the supper ellipse algorithm used within this worksheet as it has been improved for this horn type. As I generally generate the point clouds inside the VBA code by calculating each single point as a mathematical operation it was quite a challenge to get evenly distributed points along the super ellipse for each layer or spline especially for higher Lamé exponents. Various mathematical publications deal with this topic and I can only say that there is no trivial solution. Finally, different mathematical operations and numerical strategies need to be used to get acceptable results. After a lot of fine tuning of the VBA code the distribution of points is now acceptable even and smooth for higher exponents. Here is an example for an Lamé exponent of 12:
If you ever want to dive more into detail about this topic just think about trigonometrical functions with an exponent of 12 in the super ellipse formula using polar coordinates and try to rotate the polar angle by an even increment. The point distribution would be more or less disastrous along the spline. Another challenge was to correlate the two dimensional super ellipse spline with the construction wavefront. A numerical projection is used for this purpose. The clear advantage of the extra effort is the possibility to create very different horn shapes using the same algorithm and worksheet only by changing one parameter. Here are two examples on either extremes:
Indeed, DonVK preferred the native ellipse shape and I optimized a horn for him using his first target cut-off value of 425 Hz (2 inch throat). Although, I recommended a larger horn for a 2 inch driver the simulation results convinced us that this vertical is worth for making a pair as learning object. Many details about his build are posted here:
Here are again the BEM (AKABAK) simulation results for WN425-ALO-SE 2″ horn:
In the following I don’t want to lose many words but let Don’s images speak for themselves. What an ingenious and unique workflow!
I honestly admit to being a little jealous that Don is the first to have the pleasure of listening to music with this new type William Neile SE horn. Besides this the horn is optically a nice mate to his bass units imo. The listening results and power response are so encouraging that he will even build a larger horn with 270 Hz cut-off as one his next projects.
Don kindly gave me additional information on building the horn and feedback on his listening experiences for my article and allowed me to publish it. I would like to close this article with Don’s two comments.
“The R22mm mouth round over was an addition to the horn to further smooth the polar response” and “The horn’s fiberglass walls have stiffening ribs and Constrained Layer Damped (CLD) wall using silicone, sand and plaster of paris yielding final mass of ~5Kg.“
“ The WN425 was designed for my preferences with an average midrange beamwidth of 70x50deg (~1.1 sr) to match the power response of my woofer horn. The WN425 horn is very clear, and dynamic without being harsh when driven by a DE75TN from [500, 7000]Hz. The pair of horns creates a well separated and defined soundstage without drawing attention to the horn (ie. it disappears better). It’s my favourite horn, because it’s a pleasure to listen to, and I’m looking forward to building the WN270. Horns like these would not be possible without Bernd’s insight and his persistence in creating the calculator, so a well deserved and sincere thanks.”