Well, this is a bit too complicated for me
I would like to design a radial horn with an OS profile on the horizontal plan and a hypex area expansion. So to calculate the vertical profile I need to know the expansion in the horizontal plan.
I will use a planar wave model for the vertical plan (should be close enough), but I would like to use the correct model for the horizontal one.
I think I will stick with a "normal "OS profile without any radius at the mouth (I might us dense foam there if I measure anomalies, but it will probably not be too severe with a radial horn).
So my only concern for now in the expansion at the throat.
I am currently using a mix of a planar model at the throat, changing to a spherical one along the way. But this is not really precise, and not really satisfactory to begin with...
Maybe I should look at a simplified model like the Peavey quadratic one?
Humm thanks, I will try to digest that (but I might come back with questions
)Some Notes
Use that tack for the first approximation, then adjust for the area over a toroidal patch, instead of over a cylindrical segment. You have two [r]'s instead of just one. [r(x.y)] is the first, discussed in an earlier post, the second [r(x.z)], where [x] is the horn axis.
Note: As Area and [r(x.y)] are givens for a particular [x] values, you should be able to calculate [r(x.z)] and [z]. (or at least iterate and converge on solutions using Newton's Method).
It is the two long curvilinear mouth edges that should be of concern; put some lips on them. Then foam the short ones if necessary.
That begs the issue. You are morphing orifice boundaries from circular (flat disk wave front shape) to that that approximated by a toroidal patch. Squeeze flat, the cut-off end of a garden hose, while the water is running, to get some idea as to effect you are trying to create acoustically. The most important part of horn design is what you do at the ends, not between them.
You will need to get your mind around the math and geometry needed, all of which is not beyond 1st. year courses in calculus and analytical geometry.
What you are trying to accomplish is approximated by a Smith's horn design [1] and its derivatives [2]
I will provide references for these in a subsequent post.
Regards,
WHG
Well, this is a bit too complicated for me
I would like to design a radial horn with an OS profile on the horizontal plan and a hypex area expansion. So to calculate the vertical profile I need to know the expansion in the horizontal plan.
I will use a planar wave model for the vertical plan (should be close enough), but I would like to use the correct model for the horizontal one.
Use that tack for the first approximation, then adjust for the area over a toroidal patch, instead of over a cylindrical segment. You have two [r]'s instead of just one. [r(x.y)] is the first, discussed in an earlier post, the second [r(x.z)], where [x] is the horn axis.
Note: As Area and [r(x.y)] are givens for a particular [x] values, you should be able to calculate [r(x.z)] and [z]. (or at least iterate and converge on solutions using Newton's Method).
It is the two long curvilinear mouth edges that should be of concern; put some lips on them. Then foam the short ones if necessary.
That begs the issue. You are morphing orifice boundaries from circular (flat disk wave front shape) to that that approximated by a toroidal patch. Squeeze flat, the cut-off end of a garden hose, while the water is running, to get some idea as to effect you are trying to create acoustically. The most important part of horn design is what you do at the ends, not between them.
Humm thanks, I will try to digest that (but I might come back with questions
You will need to get your mind around the math and geometry needed, all of which is not beyond 1st. year courses in calculus and analytical geometry.
What you are trying to accomplish is approximated by a Smith's horn design [1] and its derivatives [2]
I will provide references for these in a subsequent post.
Regards,
WHG
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Horn & Acoustic Lens References
As there has been some interest recently shown on the subject of Acoustic Lens design, I am including important articles on that subject here as well.
Earl has also done some work is this area.
His paper is available here:
AES E-Library Acoustic Lens, Their Design and Application
Note to the forum police: The attached articles are on longer protected by copyright law due to their age.
[1] Smith's Horn (AEM-14, -20, -39)
[2] Yuichi’s Audio Lab (Radial Horn Derivatives)
Speaker Drawings
[3] Acoustic Lens Articles
Kock & Harvey (ASAJ...)
Frayne & Locanthi (SMPTRJ....)
As there has been some interest recently shown on the subject of Acoustic Lens design, I am including important articles on that subject here as well.
Earl has also done some work is this area.
His paper is available here:
AES E-Library Acoustic Lens, Their Design and Application
Note to the forum police: The attached articles are on longer protected by copyright law due to their age.
[1] Smith's Horn (AEM-14, -20, -39)
[2] Yuichi’s Audio Lab (Radial Horn Derivatives)
Speaker Drawings
[3] Acoustic Lens Articles
Kock & Harvey (ASAJ...)
Frayne & Locanthi (SMPTRJ....)
I've tried to express the area expansion in some simple way. Obviously, there is a difficulty near the throat (radius of the spherical cap goes to infinity). To avoid the struggle with OS coordinates, my thinking to overcome this was as follows. The contour function (i.e. hyperbola) can be expresed as a weighted sum of constant and linear function (Eq.1). The weights A and (1-A) are also functions of x (Eq.2). My guess is that the area can be expressed in some similar way but I haven't the time to elaborate on that. Maybe someone will catch. Whether it's even possible, I don't know at the moment.
Attachments
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I don't think that it is impossible or probably even that difficult to find the rate of change of the wave front area with distance for an OS waveguide. I just fail to see the use of such an equation. This form could only be useful in Webster's equation which is defined by the rate of change of area. But it is well known that Webster's equation is wrong, so what is the point? You will also find that the area equation has two terms. Having tried two term forms in Webster's equation before, it is difficult to solve - there is no closed form solution possible. Basically I see the whole thing as kind of a dead end.
Pointless Effort
Earl, I agree with you. Doing this would be incidental to modeling horn acoustics: a much more daunting task [1].
For an experimental radial horn just take two hyperbola pairs, defined by the coverage angles desired, [Øh] & [Øv], for the horn boundaries, and don't worry about area expansion. Just extend the curves out far enough so that the mouth is big enough to pass the lowest frequency of interest with negligible response ripple. Then morph the throat from circular to rectangular using declining fillet radii.
Note: The [Øv] pair is swept through the angle [Øh] to form a radial horn.
Have you tried this? Is so, how did it sound? How did it measure?
Regards,
Bill
Reference
[1] Freehafer's 'Hyperbolic Horn" Thesis from MIT (Circa 1937).
If you would like a copy (PFD) let me know.
Earl, I agree with you. Doing this would be incidental to modeling horn acoustics: a much more daunting task [1].
For an experimental radial horn just take two hyperbola pairs, defined by the coverage angles desired, [Øh] & [Øv], for the horn boundaries, and don't worry about area expansion. Just extend the curves out far enough so that the mouth is big enough to pass the lowest frequency of interest with negligible response ripple. Then morph the throat from circular to rectangular using declining fillet radii.
Note: The [Øv] pair is swept through the angle [Øh] to form a radial horn.
Have you tried this? Is so, how did it sound? How did it measure?
Regards,
Bill
Reference
[1] Freehafer's 'Hyperbolic Horn" Thesis from MIT (Circa 1937).
If you would like a copy (PFD) let me know.
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Bill
I have never made a device with a rectangular cross section. It just doesn't make any sense to me to do that since the source is not rectangular. I have made elliptical section devices and they work just as expected, but are significantly harder to work with and in the end I found little to no advantage in doing so. I just stick with round. They may look boring, but I have not found anything that works better.
It was fun reading the Koch and Harvey paper again - its been a long time since I had read it. Thanks for posting it.
I would like an electronic copy of Freehafer's thesis. Thanks
I have never made a device with a rectangular cross section. It just doesn't make any sense to me to do that since the source is not rectangular. I have made elliptical section devices and they work just as expected, but are significantly harder to work with and in the end I found little to no advantage in doing so. I just stick with round. They may look boring, but I have not found anything that works better.
It was fun reading the Koch and Harvey paper again - its been a long time since I had read it. Thanks for posting it.
I would like an electronic copy of Freehafer's thesis. Thanks
I can see that my idea is not very well received: it is okay, and probably spot on, but I'd like to pursue a little bit further nonetheless
My suggestion would be that you try and understand why the people who have done this stuff their whole lives do things the way that they do. Trying to "branch out on your own" is not likely to be very effective till you understand why things are the way they are now.
Absolutely.
My step kids are eleven and thirteen, and have a keen interest in art.
I'm having a heck of a time trying to get them to understand that the best way to get good at *anything* is to copy those that came before you. Engineering, art, music, basketball, whatever. 'Branching out on your own' is fun, but improving upon an existing design works better.
I think that they don't want to copy because they feel like it's somehow "dishonest" or something.
Well, this is a bit too complicated for me
I would like to design a radial horn with an OS profile on the horizontal plan and a hypex area expansion. So to calculate the vertical profile I need to know the expansion in the horizontal plan.
I will use a planar wave model for the vertical plan (should be close enough), but I would like to use the correct model for the horizontal one.
I have a Pyle horn that is somewhat similar to this. The walls are straight sided in the horizontal axis and the walls are basically exponential in the vertical plane. Not the exact same thing as hypex, but similar.
Pyle PH714
I'm not super-enthused about the sound. It's not bad by any means, but the OS waveguides and their clones sound more "open" to me. Basically the sound isn't locked to the cabinet like it is with a horn. It's "airier"
Parent Memo
We are all pigmies standing on the shoulders of giants. Something new under the sun is a rare find indeed. And the "not invented here" syndrome, sometimes is hard to overcome. But once armed with the tools knowledge provides, a breakout sometimes does occur when the status quo is challenged.
When this happens, the magnitude of concomitant change is typically huge.
We all learn by our mistakes. That is the nature of the process. Let your children explore alternatives and error while doing so. Your role is to be the moderator.
Regards,
WHG
We are all pigmies standing on the shoulders of giants. Something new under the sun is a rare find indeed. And the "not invented here" syndrome, sometimes is hard to overcome. But once armed with the tools knowledge provides, a breakout sometimes does occur when the status quo is challenged.
When this happens, the magnitude of concomitant change is typically huge.
We all learn by our mistakes. That is the nature of the process. Let your children explore alternatives and error while doing so. Your role is to be the moderator.
Regards,
WHG
I got involved helping a professional artist with a philanthropic project involving middle school kids. Sometimes they copy or make variations on some of his work, sometimes not. But to make a successful piece, they have to know how to use colors and brush strokes, transparent vs opaque, what paints to apply in what order, etc.. That stuff anyone can learn and must, before they start winging it.
Sheldon
Notice
But nevertheless in the beginning, an advancement remains driven by a suspicion that the status quo is wrong.
Earl,
A copy of Freehafer's MIT DD has been sent to your GedLee email address.
Regards,
Bill
But nevertheless in the beginning, an advancement remains driven by a suspicion that the status quo is wrong.
Earl,
A copy of Freehafer's MIT DD has been sent to your GedLee email address.
Regards,
Bill
OS Radial Horn Revisited
Sent
Arguments for a radial OS Horn (with narrower vertical OS section swept out by following the locus of an elliptical segment in the horizontal plane:
1) A cross section would not be rectangular. it would look like a bow tie.
2) Only Sections of an elliptical cylinder cutting through the horn vertically would have Rectangular Boundaries far away from the horn throat to allow for a gradual transformation from flat disk to approximating OS patch.
3) As there is a cylindrical shaped aperture of two differing dimension expanding at differing rates, as apposed to just one for the circular section horn, HOM's should be diversified and less energetic.
4) As more horn surface area is in contact with the propagating wave, a higher degree pattern control (guidance) would be provided by the horn.
5) While the driver diaphragm is round the audition space (room) is not. For a short throw horn a dispersion pattern wider in the horizontal plane than that in the vertical plane is desirable.
Regards,
Bill
Sent
Arguments for a radial OS Horn (with narrower vertical OS section swept out by following the locus of an elliptical segment in the horizontal plane:
1) A cross section would not be rectangular. it would look like a bow tie.
2) Only Sections of an elliptical cylinder cutting through the horn vertically would have Rectangular Boundaries far away from the horn throat to allow for a gradual transformation from flat disk to approximating OS patch.
3) As there is a cylindrical shaped aperture of two differing dimension expanding at differing rates, as apposed to just one for the circular section horn, HOM's should be diversified and less energetic.
4) As more horn surface area is in contact with the propagating wave, a higher degree pattern control (guidance) would be provided by the horn.
5) While the driver diaphragm is round the audition space (room) is not. For a short throw horn a dispersion pattern wider in the horizontal plane than that in the vertical plane is desirable.
Regards,
Bill
