 
|
Audio Asylum Thread Printer Get a view of an entire thread on one page |
For Sale Ads |
|
|
Audio Asylum Thread Printer Get a view of an entire thread on one page |
For Sale Ads |
194.214.158.221
In Reply to: RE: Working online Tractrix calculator-help needed posted by GM on July 09, 2008 at 09:06:47
Hello,The nearest conventional ( = old) profile to the Le Cléac'h profile is the Kugelwellen horn. (here compared among with other profiles to the Tractrix and T = 1 Le Cléac'h horn ).
Notice that the Kugelwellen follows the same logic as the Tractrix ("constant speed" translation of spherical cap wavefronts of a constant radius along the axis. The radius used for the Kugelwellen being 2 times the radius used for the Tractrix).
A main difference between the Tractrix and the Kugelwellen is that the Kugelwellen expansion is exponential all along but the expansion of the Tractrix (as I calculated it) departs from an exponential law near the mouth. If we recalculate the tractrix with a pure exponential expansion of spherical cap wavefronts, then we find a horn the mouth of which curves back as for the Kugelwellen. I called this a "revisited Tractrix" horn.
Best regards from Paris, France
Jean-MIchel Le Cléac'h
Edits: 07/10/08 07/10/08 07/10/08 07/10/08Follow Ups:
Hello Jean-Michel,
Thank you, your picture tells it all! When I did the comparision between yours and KW in my earlier post I only compared before turn back.One question though: The different horns must have different Fc? As far as I know a Traxtrix and an Exp has about the same mouth radius and kugelwellen and yours far bigger before they turn back for the same Fc.
See my example with a 180Hz horn with 11,64cm2 At.
Couldn´t you do a new picture but include a Le Cléac'h T=,707 as I have got the impression that this is what you recommend, and also use the same Fc. Then it would be even clearer to a layman as me.
Brgds
Lars
Hello Lars,To say that the cut off frequency of a horn is related to the (mean) diameter of its mouth is a common mistake.
In fact whatever the length of a horn having a known expansion, its cut-off is the same , BUT what differs is the ripple in the response curve which is due to the interferences between normal waves emitted by the diaphragm and propagating inside the horn with waves backreflected from the mouth to the throat.
We are still wrongly using a semiempirical rule originating from Keele who said that the ripple due to those reflections passes through a minimum when the mouth diameter is equal to the wavelength at cut-off. This is based on a model using the false assumption that the wavefronts are plane. Further studies demonstrated that such minimum doesn't exist.
The domain of application of this rule of thumb is only for cut horns (all Salmon horns must be considered as cut horns). If you use a minimum diameter equal to the wavelength at cutoff then you obtain an "acceptable" amount of ripple in the response of the horn. (acceptable for whom?)
Doing that, we link that diameter to the cut-off frequency but we cannot reverse that rule so: it is not true that the cut-off frequency is related to the diameter of the mouth.
Now, IMHO,to encouter this rippling, it is highly desireable to use quasi infinite horns like complete (= uncut) Le Cléac'h horn, complete Kugelwellen or complete Tractrix. But only the Le Cléac'h horn doesn't do any asumption on the shape of the wavefronts. In this sense it is a better design than the Kugelwellen and the Tractrix, the design of which is eroneously based on the asumption that wavefronts are spherical caps.
Best regards from Paris,
Jean-Michel Le Cléac'h
Hello Jean-Michell,Thanks for your explanation where I must agree, as most of what you say is known facts together with your enlightening conclusions of them.
I now see that the Exp in your picture is prolonged beyond the "Keele-point" to where its Am is equal to yours and KWs at longest.
About what the "Keele-point" concerns, one rule of thumb is to use the double Fc as lowest usable cutoff for midrange horns. This maybe as we generally do not accept the ripple, ;-)!
For Tractrix another rule of thumb seems to be that it couldn´t be used below the point where its length is equal to 0,5x wavelength of lowest useful frequency. Maybe this goes for all quasi infinte horns too?
About the wavefront of a tractrix not being spherical this was already concluded by Lambert in his studies presented in JAES 1954.
I was thinking of trying the Le´Cleac'h flare in a conventional 90*40 radial horn with straight sides. How bad would this approximation be compared to round or your proposed "radial" with 4th order axis of symmetry?
Brgds
Lars
Hello,
Some additional comments about your sentence:
"About what the "Keele-point" concerns, one rule of thumb is to use the double Fc as lowest usable cutoff for midrange horns. This maybe as we generally do not accept the ripple"
The recommandation to use an electric cut-off of the high pass filter one octave or so above Fc, the acoustical cut-off of the horn is not related to the ripple in the response.
When you look at the acoustical impedance of a horn you can see that at high frequency the horn is purely resistive but when the frequency falls around Fc, the cut off frequency, the acoustical reactance of the horn rises. This is the source of a subsequent rise of the group delay. Therefore for a note the fundamental of which is around Fc the harmonics of that note will arrive before the fundamental. This we want to avoid, we want the waveshape of the note the less distorted possible. This is the reason why most often we use an electrical cut-off 1,5 to 2 times Fc.
But this depends on the horn' flare. Try to simulate a Le Cléac'h horn having T = 0, you'll see that, if you can design a sharp cut-off high-pass crossover, then you can use an electrical cut-off very near of Fc because the interval of frequency inside which the reactance is not negligeible is very narrow around Fc.
Best regards from Paris, France
Jean-Michel Le Cléac'h
Hello,So many rules of thumb exist!
Some have been introduced to design the most compact horn for the lowest cut-off for an "acceptable ripple, others have been introduced for "acceptable directivity",... You may imagine other cases.
I don't like those rule of thumbs and simply doesn't care about them. I recommand to you and others to forget abouth them. We possess now powerful design tools. For horns design, Hornresp will give you an accurate prediction on the behaviour of your own design (on and off axis response, directivity, loading, impedance, influence of reflections at mouth using the wavefront simulator...) Using Hornresp we simply don't need any rule of thumb.
But this is for axisymetrical horns.
Many people want horns having a low height / width ratio. For the moment, except manufacurers who use 3D FEM or BEM analysis, no tools exist (or I don't know them) for the amateur to predict the behavior of non axysimetrical horns. The "amateur", most often thinks that we have just to apply some defomation (strain?) of the horn shape, then a round mouth will turn in an elliptic mouth (contained in a plane), in fact this is much more complicated because we want the wavefronts to be equidistant each one to the other. This means that all the points of the wavefront must be at the same curvilinear distance of the throat. ( = the mouth contour corresponding to a wavefront cannot be contained inside a plane)
If you design with equidistant wavefronts then you simply cannot obtain simple shapes. See few examples I calculated using my method (equidistant wavefronts without any asumption on their shape).
wide HF horizontal directivity JMLC horn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1532641&stamp=1212759567quasi Iwata horn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1532652&stamp=1212760839constant horizontal directivity JMLC horn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1532660&stamp=1212761603Best regards from Paris, France
Jean-Michel Le Cléac'h
Yes, your shapes are beautiful. Especially your version of the Iwata, (that I look upon as a refined radial). And surely they are theoretically perfect.
Though IRL they are not buildable without expensive tooling. Therefore I asked how bad you thought a "radial-approximation" should be? Couldn´t be worse than a Exp radial could it, ;-).
Brgds
Lars
| FAQ |
Post a Message! |
Forgot Password? |
|
||||||||||||||
|
||||||||||||||
This post is made possible by the generous support of people like you and our sponsors:
Top of Page ]
[ Contact Us ]
[ Support/Wish List ]
[ Copyright © 2013, Audio Asylum, all rights reserved ]
[ Take5 ]
