Mabat uses this excellent graphic calculator.
Just move the first slider (k) to the right and see what happens.
For the TD-2001, you also may want to adjust the last 2 sliders (α and α0).
It's highly recommended to read the ATH4 manual.
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Yes, HF108 (30° exit) but I guess various drivers will do. We are already four of us in Czechia who want to test the technology so I think that's enough for now. I will make a report for sure. Then we will see. I think I shouldn't offer anything here.
Glossy finish is not even an option
JSS - you're welcome.
Just got to say ATH is great, considering I don't know anything about horn design and just clicking buttons and coming up with something that looks decent
Just tweaking the demo1.cfg and entering your suggestions for the TAD2001.
Throat.Ext.Length = 65 ; [mm]
Throat.Ext.Angle = 3.6 ; [deg]
OS.k = 5
Rollback = 1
Rollback.StartAt = 0.6
Rollback.Angle = 180
Does this look alright?
J
Just tweaking the demo1.cfg and entering your suggestions for the TAD2001.
Throat.Ext.Length = 65 ; [mm]
Throat.Ext.Angle = 3.6 ; [deg]
OS.k = 5
Rollback = 1
Rollback.StartAt = 0.6
Rollback.Angle = 180
Does this look alright?
J
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This statement is incorrect and here is why. One cannot find solutions to Webster's eq. such that "equipressure and equiphase surfaces propagating inside the horn that should follow the expansion law solution of Webster’s equation" because such solutions do not in general exist. The problem is that Webster assumed that the wavefronts were planar and derived his equation from this assumption, so it never had any chance of finding the solutions that were proposed. This can be further seen by using the know exact solution of the OS waveguide. Inserting this solution into Webster's Eq shows that it is not a solution. Exact waveguide solutions require a different Diff. Eq. (the wave equation in OS coordinates) that does not assume plane waves, and this is only the same as Webster's Eq. for a single coordinate system, spherical.
Glossy finish is not even an option
Good, because imho the surface of a horn doesn't get much better than this.
True and that's exactly why JMLC developed his own method.
I am not in favor of JMLC horns, due to the limitations regarding DI, but they clearly work as intended.
JMLC's horn physics has been extensively simulated by Bjørn Kolbrek and he, as well as others, have confirmed the theory.
I just want to be sure I still follow the discussion - what was the intention?
Here's Jean-Michel's own elucidation (copied from 'his' thread with some minor editing):
While it has been eventually said that the Le Cléac'h is based on Webster's equation, in fact the expansion law is secondary when considering the horn known as Le Cléac'h horn since David Mc Bean used to introduce this profile into Hornresp and since Bjørn Kolbrek call it that way in the second part of his paper in Audioxpress.
In fact my contribution should be looked more as a method to calculate horns than rather a new expansion.
If we start from a given expansion law for the evolution of the area of the wavefronts versus their distance, by example catenoidal or hypex or exponential, what is the difference between my method and the anterior methods?
For commodity I prefer to define the wavefront as an equiphase surface described by the ensemble of points reached at the same time by a single wave emitted at the throat.
All anterior methods rely on an hypothesis for the shape of the wavefronts. Common and false hypothesis taken for the calculation of horns is that the wavefronts are planar. Voigt took for his Tractrix horn the hypothesis of spherical cap wavefronts having a fixed radius. Kugelwellen horns are based on the same hypothesis but with a doubled radius compared to the Tractrix.
During the 70's and the beginning of the 80's I was looking at the rare published pressure fields maps inside horns ( measurements by Morse in Mac Lachlan's book, by Hitachi Labs in Jean Hiraga's book, ... ). This readings lead me to think that all the anterior methods to calculate horns were eroneous as the mesured wavefronts where neither planar neither spherical.
I had the idea that if a single wave was propagating in the case the speed of sound was constant inside the horn, the above mentioned equiphase surfaces should be parallel ( = orthogonally equidistant ) each one from the other, a feature than you don't find, by example, in Voigt's hypothesis for the design of the tractrix horn for which the wavefronts cannot be orthogonaly equidistant (because they are translated at constant “speed” along a common direction). Another requirement is that the wavefronts should reach the walls of the horn at 90°.
At the time I used to program a first profile in Basic on one of the first computer I had in my lab (a Hewlet Packard 9625 if I correctly remind). I used for that a method based on more than 1 million of discrete geometrical elements the assembly of which possess the required parallelism I was looking for. No hypothesis was done on the shape of the wavefronts, the only hypothesis was their equidistance (and a known expansion law...).
It is only after personnal computers were available that I wanted to wrote a first QuattroPro spreadsheet and many years after an Excel spreadsheet... I built the first horn using that method in 1982.
Fortunately I could replace the calculation of millions of discrete elements of the original software written in Basic into a recursive formula. Around 1995 that horn was discussed on Joenet (Sound Practices ‘s discussion list) and on the french speaking group [son-qc] and I was asked to commit a paper which one was published in issue N°6 of “Musique & Technique” a publication of the Belgian Lowther Club. In 1998 Marco Henry (Musique Concrete) used to read that paper and some time later he begun to build in France his Jerzual horns calculated by my method . Nearly at the same time, Martin Seddon in Australia begun building a large format Le Cléac’h horn (now known under reference Azura Horn AH160) and the first batch came in USA where the horn received good fame within the horns/tubes crowd. One of the first user was famous tube electronics builder Dave Slagle ( see slagle.htm )
One thing that schocked many persons when they first saw the profile calculated by this method for an hypex or an exponential horn was the rolled back mouth. Even, many people were convinced at this time that the rolled back mouth was an empirical choice I made. The truth is that it is fully “natural” and results from the combined parallelism and expansion law. Unfortunately today many persons still think (wrongly) that is is useless to curve back the mouth and that the horn can be stopped when the opening angle reaches 180°.
Another question that was often asked was why the horn is wider than all commercial horns having the same acoustical cut-off. It is because in order to reduce at maxium the reflection of waves from mouth to throat we need to open the horn at more than 180° (I recommand 360°). Doing this we can consider the horn as quasi-infinite (measurements confirmed the simulations done with that hypothesis).
There was several versions of the spreadsheet, the first ones rely on the simplified hypothesis that the curved width of a given wavefront could be estimated from the diameter of a disk having the calculated area. The last versions use a step by step estimation and are much more precise, specially near the mouth.
Best regards from Paris, France
Jean-Michel Le Cléac'h
While it has been eventually said that the Le Cléac'h is based on Webster's equation, in fact the expansion law is secondary when considering the horn known as Le Cléac'h horn since David Mc Bean used to introduce this profile into Hornresp and since Bjørn Kolbrek call it that way in the second part of his paper in Audioxpress.
In fact my contribution should be looked more as a method to calculate horns than rather a new expansion.
If we start from a given expansion law for the evolution of the area of the wavefronts versus their distance, by example catenoidal or hypex or exponential, what is the difference between my method and the anterior methods?
For commodity I prefer to define the wavefront as an equiphase surface described by the ensemble of points reached at the same time by a single wave emitted at the throat.
All anterior methods rely on an hypothesis for the shape of the wavefronts. Common and false hypothesis taken for the calculation of horns is that the wavefronts are planar. Voigt took for his Tractrix horn the hypothesis of spherical cap wavefronts having a fixed radius. Kugelwellen horns are based on the same hypothesis but with a doubled radius compared to the Tractrix.
During the 70's and the beginning of the 80's I was looking at the rare published pressure fields maps inside horns ( measurements by Morse in Mac Lachlan's book, by Hitachi Labs in Jean Hiraga's book, ... ). This readings lead me to think that all the anterior methods to calculate horns were eroneous as the mesured wavefronts where neither planar neither spherical.
I had the idea that if a single wave was propagating in the case the speed of sound was constant inside the horn, the above mentioned equiphase surfaces should be parallel ( = orthogonally equidistant ) each one from the other, a feature than you don't find, by example, in Voigt's hypothesis for the design of the tractrix horn for which the wavefronts cannot be orthogonaly equidistant (because they are translated at constant “speed” along a common direction). Another requirement is that the wavefronts should reach the walls of the horn at 90°.
At the time I used to program a first profile in Basic on one of the first computer I had in my lab (a Hewlet Packard 9625 if I correctly remind). I used for that a method based on more than 1 million of discrete geometrical elements the assembly of which possess the required parallelism I was looking for. No hypothesis was done on the shape of the wavefronts, the only hypothesis was their equidistance (and a known expansion law...).
It is only after personnal computers were available that I wanted to wrote a first QuattroPro spreadsheet and many years after an Excel spreadsheet... I built the first horn using that method in 1982.
Fortunately I could replace the calculation of millions of discrete elements of the original software written in Basic into a recursive formula. Around 1995 that horn was discussed on Joenet (Sound Practices ‘s discussion list) and on the french speaking group [son-qc] and I was asked to commit a paper which one was published in issue N°6 of “Musique & Technique” a publication of the Belgian Lowther Club. In 1998 Marco Henry (Musique Concrete) used to read that paper and some time later he begun to build in France his Jerzual horns calculated by my method . Nearly at the same time, Martin Seddon in Australia begun building a large format Le Cléac’h horn (now known under reference Azura Horn AH160) and the first batch came in USA where the horn received good fame within the horns/tubes crowd. One of the first user was famous tube electronics builder Dave Slagle ( see slagle.htm )
One thing that schocked many persons when they first saw the profile calculated by this method for an hypex or an exponential horn was the rolled back mouth. Even, many people were convinced at this time that the rolled back mouth was an empirical choice I made. The truth is that it is fully “natural” and results from the combined parallelism and expansion law. Unfortunately today many persons still think (wrongly) that is is useless to curve back the mouth and that the horn can be stopped when the opening angle reaches 180°.
Another question that was often asked was why the horn is wider than all commercial horns having the same acoustical cut-off. It is because in order to reduce at maxium the reflection of waves from mouth to throat we need to open the horn at more than 180° (I recommand 360°). Doing this we can consider the horn as quasi-infinite (measurements confirmed the simulations done with that hypothesis).
There was several versions of the spreadsheet, the first ones rely on the simplified hypothesis that the curved width of a given wavefront could be estimated from the diameter of a disk having the calculated area. The last versions use a step by step estimation and are much more precise, specially near the mouth.
Best regards from Paris, France
Jean-Michel Le Cléac'h
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Looks like standard 3d printing pattern.
Here is one. Maybe not as pretty but the pattern is the same.
Nautilus speaker by bberkel - Thingiverse
So, what was the intention?
The intention, purpose if you wish, of JMLC's method is to calculate/design horns that provide the smallest reflectance and diffraction, a smooth pressure field and subsequently (due to the 'natural' expansion) generate a very low amount of HOMs.
"When calculating a Le Cléac'h horn, there is nothing special in my spreadsheets or software related to the curvature of the mouth. The curved back mouth is not intended nor provoked, it is the result of the "design by nature" of the horn."