Okay about 1 1/2 to 1, not a really wide ellipse. Can you measure any of the pattern flip that is usually associated with that type of shape or is it close enough to round that it isn't evident? By that I mean a sudden change in the vertical pattern below a certain frequency. Perhaps the large round over hides that phenomena so it isn't apparent.
That's simply not the case. The critical bands vary in width across the frequency spectrum going from about 1/3 octave at LFs to about 1/20th octave nearing 10 kHz. Look up critical bands according to Zwicker and Moore. Moore's are much narrower than Zwicker's, but are based on more recent and probably more accurate data. In my software I use exactly Moore's ERB (Equivalent Rectangular Bandwidth.), so the smoothing varies with frequency. My software also has the option of using fixed (1/3, 1/6, 1/12, 1/24), Zwicker, Moore or none.
I've built such devices, but any improvements that I saw did not justify the additional complexity and cost.
If the time synch is not used then my scheme does not work very well since phase is important. ARTA and VACs, I assume, do not us complex field data so phase is not an issue, otherwise they too would require time synched data.
If the data is time synched then I might be able to use it, but 10 degrees near the forward axis is pretty coarse. I plot in 2 dB steps, with about 1 degree of angular resolution, so much finer than either of your two plots.
But it is obvious that there is a resonance at just above 6 kHz. This is not diffraction because it does not vary with the angle. It could be a resonance across the mouth which would exist if you have such a small mouth flare radius. But it is clearly not diffraction because it exists at all off axis point in almost the same amount. It could also easily be a resonance in the waveguide structure itself. Other than that the curves look pretty good.
The pattern flip occurs because the mouth widths differ in the horizontal and vertical directions, it is not a function of the ellipse per see. For example, if one were to make the waveguide mouth round but the waveguide elliptical - by varying the mouth flare radius - then there would not be any pattern flip.
I posted vertical data in that thread as well. It maintains control down to around 1khz which was my intention and the reason I sized it the way I did. The elliptical shape was chosen to mitigate the axial dip seen in an axisymmetric wg and to reduce ctc a bit.
You have data of mine posted in your database (different speaker) that I'm pretty sure has no time lock. I've never been able to get that to work in Holm with the way I need to process audio through the DSP sw on my pc. I'll see if I can't get my living room opened up and do some measurements sometime this week as I'm curious to see how it looks with your sw......otherwise I might just send you what I've got and you can do what you like, thanks.
Did you mean to say make the wg mouth elliptical by varying the radius and keep the wg round..........and is this what you're doing on the Abbey?
So Earl if you were to make an elliptical mouth radial type horn with say a 3 to 1 ratio and used a large radius round-over you wouldn't see the pattern flip as you would see in a typical rectangular radial horn with no edge radius? Is it the large end radius termination that removes the flip from the equation?
No, I said what I mean, but you are right the NA-12 does have a non-symmetric mouth with a symmetric waveguide. But the other way around works too.
I don't know what would happen in the case you stated, that's not what I stated.
Smooth Horn Profiles using a C-Bezier Transistion Curve
The attached paper (1) provides the necessary mathematical rigor to generate a C-Bezier Curve, C-shaped in profile that will match radius of curvature [R] and tangent angle [a] of the two junction points necessary to form the profile of a horn throat adapter or a mouth bell. Actually you could model an entire horn using this regime to determine its profile using shape optimization methodologies (Uppsala & Adelaide). Note that this curve can follow exactly the locus of any conic section, hyperbola, circle, and ellipse as well. To form the mouth of a hyperbolic horn, at the point of departure from the hyperbola, calculate the tangent angle and radius of curvature, then set the radius of curvature and roll-back tangent angle for/at the desired mouth diameter and location. From these parameters a smooth transition curve may be drawn that maintains curve continuity between it and an existing horn profile to which it is joined.
[1] Joining Circular Arcs by a Single C-Bezier Curve with Shape Parameter
The attached paper (1) provides the necessary mathematical rigor to generate a C-Bezier Curve, C-shaped in profile that will match radius of curvature [R] and tangent angle [a] of the two junction points necessary to form the profile of a horn throat adapter or a mouth bell. Actually you could model an entire horn using this regime to determine its profile using shape optimization methodologies (Uppsala & Adelaide). Note that this curve can follow exactly the locus of any conic section, hyperbola, circle, and ellipse as well. To form the mouth of a hyperbolic horn, at the point of departure from the hyperbola, calculate the tangent angle and radius of curvature, then set the radius of curvature and roll-back tangent angle for/at the desired mouth diameter and location. From these parameters a smooth transition curve may be drawn that maintains curve continuity between it and an existing horn profile to which it is joined.
[1] Joining Circular Arcs by a Single C-Bezier Curve with Shape Parameter
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1) Transparent ...
... but not necessarily simple.
2) What is obvious from your comment is:
a) that you did not read the paper
or
b) that you did read the paper, but don't understand it.
3) I am aware of the line drawing tools available in most CAD programs. My design tools include Auto-CAD and MicroStation, and have done client work on a other design platforms as well.
4) All variants of the Bezier Curve are NOT the same. C-Bezier curves will exactly follow the loci of all the conic sections; others will not, and the latter is what you are likely to find in a typical CAD program. That is why I present this paper here.
5) It helps to understand the math behind the function, so you are able use it intelligently.
WHG
... but not necessarily simple.
2) What is obvious from your comment is:
a) that you did not read the paper
or
b) that you did read the paper, but don't understand it.
3) I am aware of the line drawing tools available in most CAD programs. My design tools include Auto-CAD and MicroStation, and have done client work on a other design platforms as well.
4) All variants of the Bezier Curve are NOT the same. C-Bezier curves will exactly follow the loci of all the conic sections; others will not, and the latter is what you are likely to find in a typical CAD program. That is why I present this paper here.
5) It helps to understand the math behind the function, so you are able use it intelligently.
WHG
WHG,
I'll have to go to one of my books on Solidoworks but I do believe that with a Parasolids kernel it does use a form of Bezier curve fit function on a spline with tangent end conditions. I would assume a conic section follows a simple slope function, no curvature along the X, Y axis rotated about the Z axis. It seems to me you are making this more complex than it truly is with a simple conic horn section.
And no I just looked quickly at the paper at this point. It would be much easier to read if I could print out the paper but I need some ink for my printer.
ps. After looking a little more at that paper I think you are taking that completely out of context. That is a curve fit between curved sections at both end, that is far from what you would have with a compression drivers conic end section internally and a conic horn section. You are joining two conic sections of different slopes, not two different radius curves. As far as I am concerned you would only change slightly the top octave of the passband by changing the distance between the end of the compression driver and the distance to the conic section of the horn that you chose. If you want to talk about other than a conic horn section then everything changes and the notion of any true constant directivity is again purely semantic.
I'll have to go to one of my books on Solidoworks but I do believe that with a Parasolids kernel it does use a form of Bezier curve fit function on a spline with tangent end conditions. I would assume a conic section follows a simple slope function, no curvature along the X, Y axis rotated about the Z axis. It seems to me you are making this more complex than it truly is with a simple conic horn section.
And no I just looked quickly at the paper at this point. It would be much easier to read if I could print out the paper but I need some ink for my printer.
ps. After looking a little more at that paper I think you are taking that completely out of context. That is a curve fit between curved sections at both end, that is far from what you would have with a compression drivers conic end section internally and a conic horn section. You are joining two conic sections of different slopes, not two different radius curves. As far as I am concerned you would only change slightly the top octave of the passband by changing the distance between the end of the compression driver and the distance to the conic section of the horn that you chose. If you want to talk about other than a conic horn section then everything changes and the notion of any true constant directivity is again purely semantic.
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"Ink" for Your Printer
It is the horn profile we are dealing with here. Once its geometry has been established, it is rotated about the designated axis to form surface of an axisymmetric horn body. For an OS horn the profile is a hyperbola (a specific conic section) which approaches but only becomes a straight line at infinity. The ideal curve to use to depart from this geometry should not introduce discontinuities in horn profile curvature. To do this, use a transition curve to avoid such discontinuities that will otherwise be introduced. That is the issue plain and simple. WHG
It is the horn profile we are dealing with here. Once its geometry has been established, it is rotated about the designated axis to form surface of an axisymmetric horn body. For an OS horn the profile is a hyperbola (a specific conic section) which approaches but only becomes a straight line at infinity. The ideal curve to use to depart from this geometry should not introduce discontinuities in horn profile curvature. To do this, use a transition curve to avoid such discontinuities that will otherwise be introduced. That is the issue plain and simple. WHG
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WHG,
I designed and developed hyperbolic horn shapes long ago, I do understand what can be accomplished with those shapes and I was doing that development with radial horns to correct the errors that were common to all radial horn designs at the time. This is what caused the pinched throat of any radial horn at the time, a discontinuity between the throat section and the horn flare. Mathematically they were always done incorrectly but it was expedient to produce the tooling that way. I was working with what I called hyperbolic exponential elliptical radial horn shapes long before I ever saw anyone else propose that idea. this was in 1976. There were no computer programs to do that and the math was not simple as we were working with elliptical shapes and it was all calculus.
Now when we are talking about what most say are conic horn shapes those are not typically an Oblate Spheroid, but a simple planar flat walled conic section. This is what Danley and others are doing to produce what they call constant directivity horns, not a horn with any curvature to the flare, that will never produce a true constant directivity across the entire bandwidth. All frequencies must see the same constant wall angle to conceivably produce a true constant directivity, anything else is as I say purely a semantic argument. It can only be accomplished with an infinite horn at that, so this is all just a silly argument. It truly is impossible, every horn shape is a compromise and all we can do is make the best compromises possible.
I designed and developed hyperbolic horn shapes long ago, I do understand what can be accomplished with those shapes and I was doing that development with radial horns to correct the errors that were common to all radial horn designs at the time. This is what caused the pinched throat of any radial horn at the time, a discontinuity between the throat section and the horn flare. Mathematically they were always done incorrectly but it was expedient to produce the tooling that way. I was working with what I called hyperbolic exponential elliptical radial horn shapes long before I ever saw anyone else propose that idea. this was in 1976. There were no computer programs to do that and the math was not simple as we were working with elliptical shapes and it was all calculus.
Now when we are talking about what most say are conic horn shapes those are not typically an Oblate Spheroid, but a simple planar flat walled conic section. This is what Danley and others are doing to produce what they call constant directivity horns, not a horn with any curvature to the flare, that will never produce a true constant directivity across the entire bandwidth. All frequencies must see the same constant wall angle to conceivably produce a true constant directivity, anything else is as I say purely a semantic argument. It can only be accomplished with an infinite horn at that, so this is all just a silly argument. It truly is impossible, every horn shape is a compromise and all we can do is make the best compromises possible.
Tangential Argument
Without curvature you will be left with at least two acoustically sharp diffraction edges one at throat entry and another at the mouth exit. That design is called a megaphone and was used by cheerleaders while yelling 'honkey' slogans to the crowd a long time ago. A horn will always be bandwidth limited by its dimensions. The notion that horn curvature is root cause of acoustic beaming is utter nonsense. In some good designs, it is because of it that dispersion is enhanced, not degraded. The reason why Tom's horns are straight sided, has more to do with manufacturing cost and material limitations than acoustics. He is after a point source to cover large audiences from a distance, so his trade-off set is different than that of other non-PA applications. WHG
Without curvature you will be left with at least two acoustically sharp diffraction edges one at throat entry and another at the mouth exit. That design is called a megaphone and was used by cheerleaders while yelling 'honkey' slogans to the crowd a long time ago. A horn will always be bandwidth limited by its dimensions. The notion that horn curvature is root cause of acoustic beaming is utter nonsense. In some good designs, it is because of it that dispersion is enhanced, not degraded. The reason why Tom's horns are straight sided, has more to do with manufacturing cost and material limitations than acoustics. He is after a point source to cover large audiences from a distance, so his trade-off set is different than that of other non-PA applications. WHG
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Been there, done all that ...
... and C-Bezier curve works as described and implements it all.
For the JBL ICW horn its is another matter.
WHG
... and C-Bezier curve works as described and implements it all.
For the JBL ICW horn its is another matter.
WHG
WHG,
You sure can misread what I am saying. I did say a curvature between the conic section of the compression driver and the angle of the horn. I am not saying a horn can not have a curvature to the wall but if you want to talk constant directivity then you are using semantics here. Earls shape gives the most smooth response that he could come up with and still it needed the radius at the mouth to function without the diffraction that every other horn has with a sharp termination. You can argue with me all you want, I've done this for far to long. Every horn shape known is a compromise in some way, there are no constant directivity horns, just doesn't happen even with the OS shape. Smoothly changing directivity is not constant. Earl did nothing different than I was doing in 1975, sorry but we came to very similar conclusions, chose what you like and use it, just don't use semantics to make a point. Earl filed the patent and wrote an excellent treatise to scientifically state his case, I will give him that. But what he did was not a secret to me, I was doing the same type of development before I ever heard his name or saw his papers. Simultaneous development is what it was. The fact of the matter is that hyperbolic shape change was proposed long before Earl or I ever thought of making a horn lens using that type of mathematics.
You sure can misread what I am saying. I did say a curvature between the conic section of the compression driver and the angle of the horn. I am not saying a horn can not have a curvature to the wall but if you want to talk constant directivity then you are using semantics here. Earls shape gives the most smooth response that he could come up with and still it needed the radius at the mouth to function without the diffraction that every other horn has with a sharp termination. You can argue with me all you want, I've done this for far to long. Every horn shape known is a compromise in some way, there are no constant directivity horns, just doesn't happen even with the OS shape. Smoothly changing directivity is not constant. Earl did nothing different than I was doing in 1975, sorry but we came to very similar conclusions, chose what you like and use it, just don't use semantics to make a point. Earl filed the patent and wrote an excellent treatise to scientifically state his case, I will give him that. But what he did was not a secret to me, I was doing the same type of development before I ever heard his name or saw his papers. Simultaneous development is what it was. The fact of the matter is that hyperbolic shape change was proposed long before Earl or I ever thought of making a horn lens using that type of mathematics.