# Ellipsoidal Wave Fronts in Horns

As you might already guess by the name of this website, the spherical wave horn inspired my work a lot. If we assume expanding spherical wave fronts in round horns and want to stretch the round profile to an ellipse then we must inevitably think about ellipsoidal surface areas and of course the associated mathematics. My own learning phase was not easy either, until I found myself able to mathematically master the challenge. I will describe the results of my work in this post and try to give as many details as possible and describe as much math as necessary. The whole stuff is quite complicated and therefore we will simply start with the two-dimensional part and then gradually come to the ellipsoidal surfaces.
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# A Normalized Stereographic Projection for Spherical Horns

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)

# Just another HiFi blog?

Rather not. This blog is intended to give my work on horns a suitable frame and to present information in a coherent form.

I remember very well my first experiences with horn loudspeakers and was fascinated by their sound from the first moment on. These experiences were based on the visit of various HiFi shows or special demonstrations. Inevitably one meets also the usual representatives of round horns, i.e. Tractrix, JMLC or similar/equal to Klangfilms spherical wave horn (Kugelwellenhorn). An awesome and almost comprehensive overview about the Kugelwellenhorn can be found here: Ref. 1.