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Thread: Horn / Waveguide Contour Comparisons

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    Member linear's Avatar
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    Horn / Waveguide Contour Comparisons

    This thread is to share information about the shape and performance of the various horns and waveguides that may be of interest to DIYers. This follows on from my thread “Handmade Ersatz M9500 Speakers”, which my be found at:

    http://audioheritage.org/vbulletin/s...ad.php?t=12390

    The above thread generated some spirited discussion, and provided some useful information on Horns and Waveguides. Hopefully, that can be continued here.

    To get things rolling, I am attaching two graphs which compare the contours of Conical, Exponential, Hyperbolic, Tractrix, and Hughes (Peavey) horns / waveguides. Some information on these types may be found in the above thread, including a paper by Charles Hughes on his “combination” waveguide.

    It is important to note that with the exception of the Tractrix, all of these contours have 3 degrees of freedom. This means that one may choose a throat diameter, a mouth diameter, and a length (i.e. depth), and a solution may be calculated. Of course, extremely shallow (i.e. short) horns will have extreme “flare factors”, but they will nevertheless be part of that family of contours. However, the Tractrix only has 2 degrees of freedom. Therefore, if one chooses the throat diameter to start, then only one other choice remains. If a particular length is selected, then the mouth diameter is defined by the equation. Or, one can select a desired mouth dimension, and end up with the length specified by the Tractrix formula. This paragraph is the reason for the two graphs, as will be seen below.

    My favorite horn dimensions are 2” throat diameter, 15.5” mouth diameter, and a length (depth) of 6”. This allows the horn (waveguide) to “match” a standard 15” bass driver in size, have the same bolt hole pattern, and perhaps even be retro-fitted into an existing “dual 15” cabinet. I used this configuration in my M9500 speakers described in the above referenced thread. Therefore, the first graph below follows these dimensions. My actual horn is exponential, and the others are calculated using the same parameters. The hyperbolic has a “degree of hyperbolic expansion” (M) of 0.4. (M is an additional parameter in the hyperbolic equation that can be used to shape that family of contours.) However, since we have defined the length (depth) of this horn at 6”, the Tractrix will probably not have the same mouth diameter as the others. It doesn’t – it’s 9.5” diameter at the mouth, instead of 15.5”. This is not really a “fair” comparison for the Tractrix, so the second graph shows a Tractrix with a throat of 2” dia, a mouth of 15.5”, and an equation-calculated length (depth) of 13.52”. All the other contours, on the second graph, are then calculated to these dimensions. Such a deep horn is not practical for my application, but it does compare all the contours with identical parameters.

    Here are couple of interesting facts about the Tractrix horn. The Tractrix curve was discovered in the 1600’s, when a gentleman placed his pocket watch on a table, and pulled it along by running the other end of the chain along the straight table edge. The name, Tractrix, is derived from the Latin verb “to pull”. In 1927, P. Voight was granted a UK patent for using the Tractrix curve to produce a hemispherical wave front horn.

    Finally, there are two competing German companies, www.acapella.de and www.avantgarde-acoustic.com , that both market “spherical horns” that they claim to have “invented” in the 1970’s. Their descriptions sound like a Tractrix horn (patented in 1927!). Does anyone know if their horns are different, or is the name just a marketing ploy? Inquiring minds want to know!

    Linear

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    Quote Originally Posted by linear
    ...
    Finally, there are two competing German companies,
    www.acapella.de and www.avantgarde-acoustic.com , that both market “spherical horns” that they claim to have “invented” in the 1970’s. Their descriptions sound like a Tractrix horn (patented in 1927!). Does anyone know if their horns are different, or is the name just a marketing ploy? Inquiring minds want to know!
    The descriptions of both competitors are very "colourful" (german: blümerant), I didn't find that they "invented" the "spherical horns", but they developed their own products.
    They are talking about "Kugelwellentrichter".

    Literature is hard to find, Rösch at the KLANGFILM laboratories made investigations on the Kugelwellenlautsprecher around 1950, and a commercial product had been offered, the EURODYN-combination.

    H.Schmidt published an article "Über eine neue Lautsprecherkombination" in the magazine "Funk und Ton" (Nr.5, 1950, p.226-232), where he briefly described the mathematics of a Kugelwellenhorn. This article was referenced in a book, which I missed to note in my students time. In chapter 18 "Das Schallfeld als Zweipol und die Richtcharakteristik" Schmidt is referenced but not Voigt. Here you find an accurate derivation of the Kugelwellen mathematics.
    It is interesting to notice that the diameter of the horn mouth needs not to equal the radius of the sphere. It is set equal only for simplicity of mathematics. By different values you can manipulate the length of the horn!
    I suppose a tractrix curvature is described here.

    (I could scan the three relevant pages, although the text is german the math is quite clear.)
    ___________
    Peter

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    Member linear's Avatar
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    Quote Originally Posted by Hoerninger
    Literature is hard to find.........
    (I could scan the three relevant pages, although the text is german the math is quite clear.)
    Peter
    Thanks for the information. It looks like the Spherical and Tractrix contours are similar but different. I would like to add the Spherical curve to the graph, but I haven't been able to find the equation anywhere. Could you scan those three pages that you mentioned?

    Thanks for your help.

    Linear

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    What about the Oblate Spheroid that Dr. Geddes is a fan of?

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    Administrator Mr. Widget's Avatar
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    Quote Originally Posted by Hoerninger
    (I could scan the three relevant pages, although the text is german the math is quite clear.)
    Please do... I'd love to see (graphically after Linear has his number crunch fest) how they differ from the tractrix. As for the clarity of the math... it's been over twenty years since I have done any calculus... so I might do better with the German.

    I would love to listen to comparisons of these horns... I wonder how the tractrix/exponential comparison would be when using the tractrix mouth/length requirements. Maybe we could see some computer sims from Jack?

    In any event, thanks Linear... these comparisons are quite interesting. I think a greater exploration is indeed in order.


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    Spherical Horn / Kugelwellen - Trichter

    Quote Originally Posted by linear
    Could you scan those three pages that you mentioned?
    Quote Originally Posted by Mr. Widget
    Please do... I'd love to see (graphically after Linear has his number crunch fest) how they differ from the tractrix.
    I did it, you will find the pages at another place, so this thread will not be blown up:
    http://audioheritage.org/vbulletin/s...826#post130826
    It follows a briefing of the calculation in that mentioned paper:
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    Quote Originally Posted by Mr. Widget
    ... it's been over twenty years since I have done any calculus...
    O.k. this drawing of mine is really old (1976) , it shows that the line is closed.
    ___________
    Peter
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    Member linear's Avatar
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    Quote Originally Posted by Hoerninger
    I did it, you will find the pages at this place, so this thread will not be blown up:
    http://audioheritage.org/vbulletin/s...826#post130826
    It follows a briefing of the calculation in that mentioned paper:
    Thanks very much, Hoerninger! This Spherical Horn (Kugelwellentrichter) looks very interesting. Give me a few days, and I will do some "number crunching" and add it to the graph. Also, I want to try and get on top of the theory so that we can put the contours in context. Specifically, I will try to come up with as simple an explanation as possible, as to the differences between the Spherical Horn and the Tractrix Horn and the acoustical reasons for them.

    Also, JoshK, I will add a Oblate Spheroid (Dr. Geddes style) to the family of curves.

    The Spherical Horn may have great practical significance for me. When I bulit my M9500 style speakers, I originally wanted to use a Tractrix Horn, but with a 13.52" length for my desired 15.5" diameter mouth, it was too long (deep) to fit in the cabinet (about 17" available, less 3" for the 1" to 2" throat adapter and less 2" for the B&C DE500 driver). So, I went with an exponential horn, like Zingali uses.

    (see http://audioheritage.org/vbulletin/s...ad.php?t=12390)

    However, a Spherical Horn with a 15.5" diameter mouth would be only 9.76" long, so it would fit in my cab! Maybe I will fire up the lathe and turn a couple of new Spherical Horns to try out. Since everything is assembled with 1/4" bolts, the Exponential and Spherical horns could be exchanged in about 5 minutes, from the front of the cab, for some A-B listening tests. Stay tuned to this thread for more info (but don't hold your breath while waiting).

    Linear

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    Member linear's Avatar
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    More Contours

    I have added two more curves to the graph of horn contours - Spherical and Oblate Spheriod. The second of these is the brainchild of Dr. Earl Geddes.

    The data points for both of these two new plots come from David J. McBean's "hornresp" program (http://www.users.bigpond.com/dmcbean/). Thanks, David for creating an excellent tool.

    Note that the Tractrix and the Spherical Horns flare out to 180 degrees at the mouth, and they both have only two degrees of freedom. Therefore, with a throat dia of 2", and a mouth dia of 15.5", a unique and different length is defined in each case - 13.52" for the former and 9.76" for the latter.

    I am working my way through the theory and equations to better understand the differences between the Tractrix and Spherical horns. Also, I will try to see if there is a more general form of the equations that is free of the "two degrees of freedom" limitation. I will report back when I have some answers, if my brain doesn't seize up first!

    Linear
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    Thank you for your elaboration.
    I'll stay tuned.
    ____________
    Peter

    PS:
    Your drawings and a closer look at the mathematics show that a tractrix horn is not a Kugelwellenhorn, which I assumed first. The Tractrix curve, which is normally used for horns, will never be closed.

    I wonder what the mathematics of a spherical horn is. I did not find anything. So I do not dare to say anymore that a Kugelwellenhorn and a spherical horn are the same.

    Regards
    Peter


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    Now I'm a little step further.
    Avantgardes american site (http://www.avantgarde-usa.com/technology.html) shows more than the german site
    ( http://www.avantgarde-acoustic.de/th...php?sprache=en ).
    These additional pictures are an indication that they are using the Theorie of the Kugelwellenhorn.
    (Compare with the thread "spherical horn / Kugelwellenhorn").
    ____________
    Peter

    PS:
    Arrg! Very hidden on the german site there is a PDF where they are naming "Kugelwellentrichter".
    http://www.avantgarde-acoustic.com/d...3902a5af95.pdf
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    Graphical comparision of Exp., Tractrix and Kugelw.

    Found this interesting thread that caught me on as I am designing a mid-horn based on the 183Hz flare of the 2441 and 2328 adapter to be used. My findings differ a little from Linears as I use the same flare. I was stunned when I found out the small differences in the first part of the horns. The horn is measured from the phaseplug of the driver.

    Up to 17cm there is less than 1% , to 29cm 2%, to 45cm 5% and to 55cm 10% difference in area.

    One will get good loading from 187Hz for the KW(Kugelwellen/Spherical), 210Hz for the Exp and 236Hz for the Tractrix. So the horn will be usable from 300Hz if you have a driver that goes that low.

    Please also note that I did not use Hornresp for the plots, instead I used the original formulas and Excel to be sure, thanks Hoerninger for the KW info.
    Last edited by reVintage; 05-29-2008 at 08:59 AM. Reason: spelling
    Brgds
    Lars

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    Super Moderator yggdrasil's Avatar
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    Keep us updated on the progress Lars. I like the size you are planning.

    Since you are looking at the 2328 adapter, I take it you are going build a horn that is not circular. What are your thoughts on the conversion, and to which format?
    Johnny Haugen Sørgård

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    I am currently thinking of two possible solutions based on the Tractrix area-expansion as I like the way it opens up. Also note that the horn will be some sort of hybrid even if this expansion is choosen.

    As the "blueprinted" 2328 converts the wavefront to 90 degree radial it must be a radial or a multicell working from 300-500Hz.

    The first model I will try is a 3-cell where the opening will be 3*30cm wide, 30cm high and 56cm long (for tractrix) with 3 square cells like below. The upper limit will be 9kHz if the bandwidth equation from the original multicell patent is valid also for Tractrix. Hopefully the fingering will be lower due to the choosen expansion.The plots is from after the 2328:

    The 90 degree radial will be composed of a 3,5cm high Smith followed by a radial much like the 2397 variations in this forum but with Tractrix expansion all the way:



    Brgds
    Lars
    Last edited by reVintage; 05-29-2008 at 11:41 PM. Reason: image in wrong place

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