William H. Geiger hat freundlicherweise seine Tabellenkalkulationsblätter allgemein verfügbar gemacht.

Excel-Sheet by W.H.Geiger, here:


Preliminary horn fold readme:

1) Sent you a horn fold generating spreadsheet, HornFold.xls, via e-mail. This should help you get rid of the sharp inside edges and allow you to compensate the flair rate for acoustic foreshortening of fold center length that occurs as an acoustic wave travels around the fold at increased velocity[1].

2) Note that 'reflectors' (to replace smoothly bent horn walls) are NOT required for transverse fold width [Wf] < [c]/(2*[fh]), where: [c] - sound velocity [fh] - highest frequency to be passed.

3) If the horn enclosure does not have a rectangular envelope, its aesthetics may improve.

Q: Does it do conical as well? Can one describe conical expansion with hyperbolic? I tried in hornresp, and the response seems equal for T=5=10=100, which in turn is equal to the response of a conical horn with same throat, mouth and length. So it works?

  • a) Salmon Family Member Cases on [m] & [T] are:

  • 0) ([m]=0) - Cylindrical (Fully Degenerative)
  • 1) ([m]>0), ([T] = oo) - Conical (Linear Flare)
  • 2) ([m]>0), (1<[T] < oo) - Bessel
  • 3) ([m]>0), ([T]=1) - Exponential
  • 4) ([m]>0), (0<[T]<1) - Hyperbolic
  • 5) ([m]>0), (T=0) - Catenoidal

  • b) Note that only horns of rectangular section are addressed by the fold-generating model. Therefore, modeling circular section horns is not possible here. The ability to specify a linear flare rate will be provided in the next model release, however.

  • c) Some of the low, [T]>1, Bessel flairs may be bent if [m] is small enough. Note that if a horn flare is ‘steep’ then folding it is not an option. As the model has not been ‘bullet-proofed’, under such conditions it just ‘blows up’.

Some more remarks by Sven: Rows 28 to 31 are absolutely necessary as they are at the present, since they describe the horn and those rows should always be the same in order to describe one particular horn. Let me use an example horn. I put >row 28: 40 Hz flare rate, >row 29: 0,434 horn shape factor >row 30: 12,27 in horn height (parallel sides) >row 31: 6,417 aperture width

The results you get when using the default values:



Cosine Transform tool by W.H.Geiger


.. for Bass Horns


Like your nomenclature better than mine: "Co-Sinusoidal Transition" so we will use yours instead.

The mission of the Cosine Transform is to provide a smooth (non-turbulent) transition that joins a circular throat aperture, at the driver, to the body of a rectangular section horn having two parallel and two divergent walls. To do this, the transform operates simultaneously over three dimensions as it follows a [Z] coordinate that serves as the horn axis. The resulting design, anticipates use on laminar construction methods to produce the resulting warped surfaces. The details of the geometric morphing that takes place along the way may be described as follows:

1) In consecutive [X],[Y] sections leading away from a circular throat aperture, the following transformations take place:

a) Aperture area is expanded according to Salmon’s horn function

b) Fillet radii are diminished to rectangular corners at the exit

c) The aspect ratio is changed from unity to that of the final rectangular exit aperture.

2) In the [Y],[Z] plane, a cosine flare is used to join to the parallel sides of the horn body that follows.

3) In the [X],[Z] plane, a modified hyperbolic flare is used that may be adjusted to achieve a near linear diminution of the fillet radii.

A new version, 5.2, to be released shortly includes:

a) A choice between inch -Y΄in‘, or centimeter ΄cm‘, units of measure.

b) AutoCAD? command script vectors for drawing the cosine and hyperbolic profiles as well as the numerous aperture sections.

That is all for now.

...and a result:


Horn mouth tool by W.H.Geiger

A description on how to use this work sheet is in it.


Tractrix horn contour by W.H.Geiger

VBA Source Code Update of Excel Spreadsheet UDF's for Tractrix Horns. See the comments for more info


Last modified: 23.2.2004 12:13:52
Home %Gβ€’%@ Edit %Gβ€’%@ Versionen %Gβ€’%@ Search %Gβ€’%@ Forum