I will continue now with a topic that seems not obviously related to horns. During my research about the spherical wave horn the first goal was to stretch the round profile into an elliptical one. More about this in a forthcoming post. Although it should be a good idea to break the symmetry, most horns on the market still have a flat mouth. If we have a look at the ellipse we have a major and a minor axis. The minor axis is generally orientated in the vertical axis of the horn mouth, thus having less mouth diameter than the horizontal axis. The same holds for any rectangle flat mouth horn and if we find a datasheet we generally observe that for low frequencies the vertical control is not the same as for the horizontal plane. The LF beaming starts earlier for the vertical direction because of less mouth diameter. Next to the mouth diameter, the horn length is another important property with respect to loading. But to achieve a better loading for a more balanced pattern control the horn length must become longer for the walls near to the minor axis and shorter near to the major axis. For a long time I had no reasonable idea how to do such a transformation until I came across with a projection procedure that is used to generate a world map. This procedure is called stereographic projection (Ref. 1, Ref. 2)

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