Unless a second speaker in the back is active or the cabinet has been designed to be cardioid, the NS-15 and the M2 would have to be nearly identical. It appears that the M2 is ported so the cardioid cabinet is not likely. But, as is shown in my book, a second speaker facing backwards could be made to create a higher LF directivity. I have thought about doing this, even did simulations, but the cost becomes huge for a very small advantage. The added speaker must have its own DSP and amp - adds a lot of cost and complexity.
I also found the dual waveguide design to be well done. I would love to include this is my database as I think that a much higher resolution on the polars would be desirable. I expect that are quite good.
I am not sure about the bass array, that's not how I would solve the problem.
Earl,
Have you ever considered an asymmetric exit mouth radius? No it wouldn't eliminate the standing way of a round symmetric horn but perhaps it could be handy in your desire for an asymmetric pattern for first wall reflections? Just thinking of the top here this morning. In the horns that I did for my strange looking speakers, my avatar, I used a four sided elliptical wall shape with the corners connected with a radius, nowhere are there parallel walls or sharp corner contours. I wonder if those would show the on axis hole you are speaking of, it has been twenty years since I last worked on those horn designs. These horns are symmetric about the axis, just not round and definitely not square. I seriously developed Hyperbolic Exponential Elliptical Radial horn designs many years ago but didn't produce them. I now wonder as I wasn't aware of the phenomena then of pattern flip if that would be and issue if the termination would include a large radius termination? I've seen some of your patented, now expired I think of so phase plug designs that were not symmetric about the axis, an idea that I also conceptualized but never pursued. I still wonder how well that could work with a matching waveguide as I just described above.
I would have pursued these things if I had not been distracted with all the product and materials development that took me away from audio for most of the last 30 years. I only got drawn back in by a challenge to develop new cone material and manufacturing method. That has lead me to where I am now working on a direct radiator device development and system design for a self powered speaker. I know one of the others I am now working with wants me to add a short waveguide to go with my dome tweeter design and that has got me thinking about things I left behind so long ago.
Have you ever considered an asymmetric exit mouth radius? No it wouldn't eliminate the standing way of a round symmetric horn but perhaps it could be handy in your desire for an asymmetric pattern for first wall reflections? Just thinking of the top here this morning. In the horns that I did for my strange looking speakers, my avatar, I used a four sided elliptical wall shape with the corners connected with a radius, nowhere are there parallel walls or sharp corner contours. I wonder if those would show the on axis hole you are speaking of, it has been twenty years since I last worked on those horn designs. These horns are symmetric about the axis, just not round and definitely not square. I seriously developed Hyperbolic Exponential Elliptical Radial horn designs many years ago but didn't produce them. I now wonder as I wasn't aware of the phenomena then of pattern flip if that would be and issue if the termination would include a large radius termination? I've seen some of your patented, now expired I think of so phase plug designs that were not symmetric about the axis, an idea that I also conceptualized but never pursued. I still wonder how well that could work with a matching waveguide as I just described above.
I would have pursued these things if I had not been distracted with all the product and materials development that took me away from audio for most of the last 30 years. I only got drawn back in by a challenge to develop new cone material and manufacturing method. That has lead me to where I am now working on a direct radiator device development and system design for a self powered speaker. I know one of the others I am now working with wants me to add a short waveguide to go with my dome tweeter design and that has got me thinking about things I left behind so long ago.
I think that ARTA can do polars like mine. There was a big discussion of this topic in another thread. But to be comparable with mine one must take ARTA data about every 5 degrees or its resolution will not be as good as mine at the upper frequencies. I use a ERB (Equivalent Rectangular Bandwidth) smoothing mechanism which ARTA cannot duplicate, but if ARTA is done at 1/24 th octave then it matches mine at the high end, but is sharper at the low end. This is probably OK, but the other way around isn't valid. ARTA does not calculate the DI or PWL for an arbitrary axis as mine does either. To me, these later two tell the most complete story.
The referenced plot is not an accurate display of reality
I n fact the measurement is very accurate as the comparison to a simple simulation shows. As I stated enclosure size is essential.
Simulation:
Measurement of M2:
Of course.
Average power response (equalized flat at 0°):
Directivity Index:
Please note that I use this horn from about 3-4 kHz upwards. It will be integrated in a 4-way design.
Attachments
The NA-12 mouth is asymmetric and there is only a minimal hole. If I found this hole to be a major issue then I would have dealt with it a long time ago. If my speakers are setup as I recommend then one is virtually never on the axis with the hole. Competitors like to point to this hole as a "flaw" but they never acknowledge that my speakers are designed to work differently than the norm, so one cannot apply "normal" criteria to them. This hole would be a problem in a center channel, but in that case I do a different crossover that minimizes the hole with a slightly degraded polar response. In the NS-15 and NA-12 the hole is not an issue in either the side speakers or the center channel, although the center always benefits from a slightly different crossover.
Thanks for the explanation.
Let me know if your're open to plot a polar with your method for me. I'm planning on measuring the horizontal polar of a huge midbass horn (1.2 m wide) either in October or November.
Thanks Earl,
I don't think anyone who really understands all the variables between speaker systems can assume there is one standard configuration. So anyone disregarding your setup information for your designs would just be a fool in my eyes or someone looking for an issue to make of a non issue.
I think the biggest issue with the majority of horn loaded systems today is only one, that is purely size. The greater market has moved to small speakers because of the many years of marketing by Bose, that marketing has really misinformed the public for so long but as they say if you repeat something long enough people do believe it. I could never own one of their products for anything beyond background music. That is what i consider most of the small dreek that is in the market today.
I don't think anyone who really understands all the variables between speaker systems can assume there is one standard configuration. So anyone disregarding your setup information for your designs would just be a fool in my eyes or someone looking for an issue to make of a non issue.
I think the biggest issue with the majority of horn loaded systems today is only one, that is purely size. The greater market has moved to small speakers because of the many years of marketing by Bose, that marketing has really misinformed the public for so long but as they say if you repeat something long enough people do believe it. I could never own one of their products for anything beyond background music. That is what i consider most of the small dreek that is in the market today.
Size Matters
That concept is not limited to just horns (and "waveguides" i.e., Freehafer's Horn). The influence an object exerts on a passing or projected acoustic wave remains a function of the difference in size between them.
It may be possible to take the technology used at the ICW throat and move it to the mouth perimeter to address reflectance and standing wave issues there while retaining the desirable characteristics of the OS throat geometry. This design tack however, will also yield potentially a larger horn as well.
While the OS horn geometry provides a desirable decline in curvature as a cone is asymptotically approached from its throat, no provision for a mouth terminus is included as an infinite extent is assumed. The curve of choice for a horn should also provide an increasing rate of curvature as the mouth is approached without introducing discontinuities in the resulting curve's second derivative.
An alternate mathematical rigor that may be employed in horn design is described it the attached paper [1] that provides additional degrees of freedom to specify an entire horn body profile in a single continuous curve or curve set. Even an ICW can be designed using a mesh of these to define its complex surface.
In any event, the acoustical application of such curves can be accomplished by use of a second technology known as Shape Optimization. This has been addressed earlier, but here is one of the more recent article [2] on this subject as well.
n.b.: There are many more articles on both subjects, I just picked two that are particularly relevant and current.
WHG
[1] http://www.math.zju.edu.cn/webpagenew/uploadfiles/attachfiles/200942733837187.pdf
[2] http://umu.diva-portal.org/smash/get/diva2:741364/FULLTEXT01.pdf
That concept is not limited to just horns (and "waveguides" i.e., Freehafer's Horn). The influence an object exerts on a passing or projected acoustic wave remains a function of the difference in size between them.
It may be possible to take the technology used at the ICW throat and move it to the mouth perimeter to address reflectance and standing wave issues there while retaining the desirable characteristics of the OS throat geometry. This design tack however, will also yield potentially a larger horn as well.
While the OS horn geometry provides a desirable decline in curvature as a cone is asymptotically approached from its throat, no provision for a mouth terminus is included as an infinite extent is assumed. The curve of choice for a horn should also provide an increasing rate of curvature as the mouth is approached without introducing discontinuities in the resulting curve's second derivative.
An alternate mathematical rigor that may be employed in horn design is described it the attached paper [1] that provides additional degrees of freedom to specify an entire horn body profile in a single continuous curve or curve set. Even an ICW can be designed using a mesh of these to define its complex surface.
In any event, the acoustical application of such curves can be accomplished by use of a second technology known as Shape Optimization. This has been addressed earlier, but here is one of the more recent article [2] on this subject as well.
n.b.: There are many more articles on both subjects, I just picked two that are particularly relevant and current.
WHG
[1] http://www.math.zju.edu.cn/webpagenew/uploadfiles/attachfiles/200942733837187.pdf
[2] http://umu.diva-portal.org/smash/get/diva2:741364/FULLTEXT01.pdf
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WHG,
It seems that the earlier horns i designed using hyperbolic function and both end conditions are fairly well matched to your requirements. I can't say they end completely flat at the mouth but very closely to that. It wouldn't take much additional length and they could easily be combined with a large roll radius termination. I think the small amount of diffraction as they are is very low. As I used them in their molded enclosures I actually had a wooden section that covered the attachment flange and created that radius and blended smoothly into the shaped body structure. Perhaps with more testing there could have been some small shape optimization changes, can't say without some serious polar response testing.
Thanks for the reference materials
It seems that the earlier horns i designed using hyperbolic function and both end conditions are fairly well matched to your requirements. I can't say they end completely flat at the mouth but very closely to that. It wouldn't take much additional length and they could easily be combined with a large roll radius termination. I think the small amount of diffraction as they are is very low. As I used them in their molded enclosures I actually had a wooden section that covered the attachment flange and created that radius and blended smoothly into the shaped body structure. Perhaps with more testing there could have been some small shape optimization changes, can't say without some serious polar response testing.
Thanks for the reference materials
Clarification
They may look smooth but they may not necessarily be so acoustically. If at the point of tangency between the two curves, their radii of curvature do not match as well, then there will be a discontinuity between their 2nd. derivatives. Also if the horn lips are acoustically small, they will continue to act as a diffraction edge. Ideally, at least three sides on the enclosure should be formed by a seamless wrapping of horn lips backward to form the enclosure body. For those waves carrying most of the energy exiting the horn, they will 'see' the entire enclosure as a baffle, not just the front, plainer, driver/horn mounting surface. This is particularly important in the c/o overlap region where both drivers are operating together.
WHG
They may look smooth but they may not necessarily be so acoustically. If at the point of tangency between the two curves, their radii of curvature do not match as well, then there will be a discontinuity between their 2nd. derivatives. Also if the horn lips are acoustically small, they will continue to act as a diffraction edge. Ideally, at least three sides on the enclosure should be formed by a seamless wrapping of horn lips backward to form the enclosure body. For those waves carrying most of the energy exiting the horn, they will 'see' the entire enclosure as a baffle, not just the front, plainer, driver/horn mounting surface. This is particularly important in the c/o overlap region where both drivers are operating together.
WHG
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Sounds that way to me. At least that's what I try to do.
Large round-overs do get to be problematic from a construction point of view. 1.5" is as large as can be cut with a shaper, about 1" with a good router. More than 1.5" would require a separate piece I believe. At least that's what my research showed.
If your using wood and have access to a large swing lathe you could do a fairly large radius. If you understand how to make fixtures you could make very large radius's with a large diameter disk sander or a router and ball nose or straight cutter. I've seen some very nice work done with a normal plunge router if the router is mounted on a moving plate with a corresponding groove cut into the fixture for the router to follow. There's not much a good woodworker can't cut when given the idea.
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I've thought in the past of building an enclosure like a boat. The baffle would be the "keel", the "ribs" would come around from it and go to the back, which would be the "deck", and the longtitudinal members cut out to interlock around the "ribs" and fiberglass or laminate veneer layers to cover the whole thing. The millwork place could supply me with some big quarter round for the top and bottom enclosure corners. Then use some kind of foam between the ribs for damping. That way I could get some really generous curves. The most dangerous tools I'd have to use would be rotary and jig saws. I made some sketches; nothing seemed impossible. It looked mighty tricky, though.
I also thought, "this way lies madness."
This helped me to put paid to the method I was looking for, to align the focal points of the H&V straight walls, even if just for the first 6". Maybe the compression chamber is a better place to take up the discrepancy (1:0.577
)
It would be logical to have a two-part assembly for the OS waveguide and round over, as the two serve different purpose and constraints.
After all the round over is not part of the OS profile, and could as well be seen as part of the enclosure, exactly like the round overs on the edges of the cabinet.
After all the round over is not part of the OS profile, and could as well be seen as part of the enclosure, exactly like the round overs on the edges of the cabinet.