Article re Tractrix Horn

[bodcaw boy]

ROY....Mike Klementovich sent me 165 pages of a study by John T Post and Elmer L Hixson....A Modeling and Measurment Study of Acoustic Horns. (May 1994) from the Electroacoustic Reasearch Labratory..Dept. of Electrical and Computer Engineering..University of Texas at Austin.....Its heavy in math & formulas..Right up your alley.....Have you read it? I can send it your way if interested.

hey how do you know mike K? do you also know maureen? va voom! (hey she has a nice car!)

have a blessed day,

roy delgado

[bodcaw boy]

Roy,

Sent you another PM.

Jordan

back at ya!

have a blessed day,

roy delgado

[ZAKO]

Mike is a great guy...A Perfusionist,... also a keyboard musicion., and all around pain....Maureen? va va voom...I never noticed her car. Both are into Klipsch speakers and dedicated tube rollers. Both are positive OK.

[D-MAN]

The link to D.B. Keele's AES papers is here: http://www.xlrtechs.com/dbkeele.com/papers.htm

Here is his patent on the modified conical horn... (attached) - if it is the 1978 EV horn, that is!

Dana

Keele_1978_EV_midrange_horn.pdf

[jorjen]

Sent you two more PM's Roy.

Best,

Jordan

[bodcaw boy]

triple j,

ping.

have a blessed day,

roy delgado

[colterphoto1]

"geesh it's crowded in here...............how did THAT get in here..................crap i forgot."

Brilliant. Does the sign on the door read: 'Mad Genius at work"?

Peace,

Michael

[mark1101]

Gil,

[mark1101]

Gil,

This is great info. For years I thought exactly the opposite of how these horns operated.

Does anyone know if the "phasing" benefits mentioned between drivers require that the tweeter also be a matched tractrix?

Next question:

If someone used extreme slope networks with an exponential horn, does that get you half way there? I mean are the phasing issues dealt with leaving just the vertical room reflections? Is this correct thinking?

Edit: ....Obviously the article does not explain how phase alignment is actually achieved with Tractrix, just that it happens...to some degree not quantified. Is there some magic that allows tractrix designs to help time align drivers, or is it just because there are less room reflections that now improved time alignment can be expected from horn systems?

Thanks

[mas]

Here is the assembled article above, converted to a single PDF doc. Hope this helps.

Thanks Gil for posting it!

Tractrix.Concat.pdf

[mas]

If someone used extreme slope networks with an exponential horn, does that get you half way there? I mean are the phasing issues dealt with leaving just the vertical room reflections? Is this correct thinking?

Edit: ....Obviously the article does not explain how phase alignment is actually achieved with Tractrix, just that it happens...to some degree not quantified. Is there some magic that allows tractrix designs to help time align drivers, or is it just because there are less room reflections that now improved time alignment can be expected from horn systems?

Thanks

Maybe Roy will comment on this a bit, but the design of the horn does
nothing to align the acoustic origins of the various separate drivers(ignoring other contributing factors such as driver Q, etc...). Rather its primary benefit is in resolving internal anomolies that result in a more optimal individual driver's response (which ultimately and subsequently may impact the interaction with other components via factors such as pattern control/Q... You simply can't escape the total context inwhich the driver acts...)

Let me see if I can clarify this hierarchy of relationships a bit (while also demonstrating that it is not a simple relationship, except to the degree that we selectively focus on an aspect of the total environmental system.)

Issue associated with superposition such as comb
filtering and the associated polar lobing can occur in various 'orders of
magnitude' or scale, ranging from the internal design of a singler component
driver, to the next order of magnitude characterized by the interaction of several individual drivers as well as virtual sources such as diffraction along with Q, crossover bandpass, slope, and acoustic center offsets, to the next order of magnitude of interaction characterized by the interaction of
assembled speaker units, up to the the level of interaction between the the speaker's output with the external environment
such as a room. And where each reflection can be modeled as aa additional virtual source along with their signal offsets in time and varying intensities. And each order of scale comprising this total relationship ideally must be addressed.

In other words, conceptually while we can treat each 'level' as a distinct and independently existing entity for the sake of simplicity and focus, in reality is that each of these levels are interactive and integrally related. And one ignores any aspect of this complex relationsip at their own peril.

The internal design can certainly minimize reflections and phase errors, etc., that
negatively impact the resultant performance of the individual driver's
response,
And this
is just what the design of the Tractrix attempts to address.

But the successful optimization of single or multiple components will not automatically eliminate the need to address the interdriver interaction in a speaker assembly, nor the higher order
interaction between speakers nor the speaker interaction with the room &/or external environment.

In other words, phase and time issues (etc.) potentially affect each individual
component as well as the interaction
of the various components, real or virtual, at each level of magnitude

Signal alignment and crossover design can be used to minimize the
interaction of separate non-coincident drivers, and signal alignment can be
employed to reduce the interaction of separate sources ( real or
virtual), but you must still be cognizant of the varying levels of interation
between the hierarchical levels – be they internal to the driver up to the
interaction of the component drivers to the interaction of an assembled speaker with other speakers and finally with the larger interaction with the room/environment itself.

It is rather like the nested Russian dolls of which you may be familiar,
where inside one you find another, and another and another....And you seldom
can afford to ignore any level of interaction.

[Chris A]

Facinating Gil! thanks for posting all this...it leads me to wonder that why, when faced with the facts about shortcoming, klipsch did not work on improving the horn design? or did they?

Have you been following any of the work by Dr. Earl R. Geddes on horn design? a friend of mine over at peavy recommended this guy as a true maverick genius in horn design (sounds little like PWK no?) let me know what you think, http://www.gedlee.com/

warm regards, tony

Well,

The above referenced web site (Geddes, et al.) has a jewel of a white paper embedded in it. I've taken the liberty of cleaning up a couple of typos that were slowing my reading. This paper is hawking his speakers, the IP of which he subsequently sold to an Asian firm which promptly stopped manufacturing them and started to apply his other IP to smaller speakers. I hope that Klipsch Corporation doesn't mind the repost here because the principles found in this paper just hit the mark on the Jubilee design for home use and the use of bass traps in smaller rooms--two for one. It's like deja vu all over again.... Read carefully, re-read if necessary. I hope that if there is anything here that is hard to understand, you'll come back to this thread and post a question or two. I'm sure someone will gently answer.

There are another couple of white papers/presentations on non-linear distortion and the human ear. These are a bit more difficult to digest, but if your math and physics are up to it, really say some things about low-distortion speakers.

Regards,

Chris A.

Cum laude.pdf

[DrWho]

Hey Chris, interesting article! I had a few random comments...

I don't agree with the author's assessment of room modes, but that's opening a whole new can of worms and I don't think it is relevant to the design of an ideal speaker anyway.

He mentions "why tractrix?" - to which I would respond, it maximizes the efficiency of the horn which means you get less distortion from the driver. It looks like Roy is minimizing "HOM" with his modified tractrix while also maintaining the increased efficiency.

Speaking of efficiency, hornloading that 15" driver is gonna bring it down even more too...of course at the expense of a bigger footprint. I really like how there were performance considerations for every aspect of the design mentioned in that article...it's the way it should be.

How much does the Cum Laude series of speakers cost? Would you happen to know what kind of crossovers are being used too?

[Chris A]

WYSIWYG on the "cum Laude" speakers - I didn't find anything else at the author's site. I suppose Google on "Audio Intelligence (Ai) of Bangkok, Thailand" might get you closer to the answers.

Note that his company has done work on psychoacoustic effects of what we call "IMD". The paper and presentation can be found at this site - http://www.gedlee.com/distortion_perception.htm (sorry about the link- "bad HTML day"). One of the surprises: IMD effects are more discernable at low signal levels than at high...interesting, if true. He also introduces a new parameter (Gm) that tracks the nonlinear psychoacoustic effects of hearing using experimental trials, basically replacing IMD and TMD as primary engineering parameters. Also interesting, if true.

This forum is almost a bottomless pit - serendipitous in this case.

Chris A.

[Edgar]

does the wave curve because of friction on the wall?  well right at the wall, the velocity should be zero so it would dictate that wave would bend.  kinda of like looking at flowing water in pipe; if you look at the model, one of the assumptions is that at the wall the velocity is zero.  have i ever seen it? no. 

Roy,

I know that I am responding to quite an old post, but I've only just read it for the first time today when the thread was updated with a new response.

Please understand that I'm an engineer, but my specialty is signal processing not acoustics, so my understanding of acoustic waveguide theory is not as complete as I'd like. That said, don't acoustic waves propagate according to Huygen's Principle? If so, then the curvature of the wave front can intuitively be explained by differences in path length. If the portion of the sound wave adjacent to the wall propagates along the wall, while the portion of the sound wave in the "center" of the horn propagates straight down the center of the horn, and both propagate at the speed of sound, then the wave front has to curve.

Maybe the easiest way to visualize this is to think of a point source in a flat baffle as a degenerate horn with instantaneous 90° flare. The wavefront will be hemispherical, not planar.

BTW; the path length "L" (along the wall) of a circular Tractrix horn is easily computed from the Tractrix defining equation as: L=a*ln(r2/r1), where a is the mouth radius and r1, r2 are radii between which you want to know the path length (this corresponds to the nomenclature used by Bruce Edgar in his 1981 Speaker Builder article). So the path length (along the wall) of an entire Tractrix horn is L=a*ln(a/r1), where r1in this case is the throat radius. From the defining equation for the Tractrix it can easily be shown that the path length is much longer than the horn itself, meaning that the portion of the sound wave that propagated down the "center" of the horn exits the mouth long before the portion that hugged the wall even reaches the mouth. Hence, the "bubble" model of horn propagation.

Greg

[WMcD]

Hi, Edgar,

I did some math on a spreadsheet.

It is possible to do a Pathagorian (sp?) analysis of the length of the wall. Then you have to crank in the actual bulge of the bubble. They come in pretty close. Try that and see if you agree.

As Roy says, tractrix wins again.

- - - - -

Sort of an aside. Voght (proponent of the tractrix which he re-discovered) was a boy genius who somehow got everything right. Maybe because he was not comtaminated by the old men. As youths we read Tom Swift, Jr. He was one of those types, in fact.

Gil

[Edgar]

It is possible to do a Pathagorian (sp?) analysis of the length of the wall.  Then you have to crank in the actual bulge of the bubble. They come in pretty close.  Try that and see if you agree.

Pythagorean. That's how I came up with the expression for path length along the wall. If the differential length dL is the hypoteneuse, with differential distances dx and dr being the legs of the right triangle, dL=sqrt(dx²+dr²); then using Bruce Edgar's expression for dr/dx=-r/sqrt(a²-r²) you get dL=(a/r)dr, and so on.

The bubble is not spherical, but rather is oblong with the longer axis in the direction of the horn axis. I have often used a spherical wave approximation for analysis, because while it's not perfect it's a much better approximation than a plane wave. The sphere has constant radius "a" and is trucated such that it contacts the horn wall perpendicular to the tangent of the wall itself.

As Roy says, tractrix wins again.

Tractrix is not perfect, though. Bruce Edgar told me that nobody uses Tractrix for bass horns because they don't provide a good load near cutoff. See http://forums.klipsch.com/forums/thread/994068.aspx for my proposed solution to that problem.

Thanks,

Greg

[bodcaw boy]

It is possible to do a Pathagorian (sp?) analysis of the length of the wall. Then you have to crank in the actual bulge of the bubble. They come in pretty close. Try that and see if you agree.

Pythagorean. That's how I came up with the expression for path length along the wall. If the differential length dL is the hypoteneuse, with differential distances dx and dr being the legs of the right triangle, dL=sqrt(dx²+dr²); then using Bruce Edgar's expression for dr/dx=-r/sqrt(a²-r²) you get dL=(a/r)dr, and so on.

The bubble is not spherical, but rather is oblong with the longer axis in the direction of the horn axis. I have often used a spherical wave approximation for analysis, because while it's not perfect it's a much better approximation than a plane wave. The sphere has constant radius "a" and is trucated such that it contacts the horn wall perpendicular to the tangent of the wall itself.

As Roy says, tractrix wins again.

Tractrix is not perfect, though. Bruce Edgar told me that nobody uses Tractrix for bass horns because they don't provide a good load near cutoff. See http://forums.klipsch.com/forums/thread/994068.aspx for my proposed solution to that problem.

Thanks,

Greg

i guess i better throw away all those good measuring, good sounding bass horns i did in the tractrix form.......

dr edgar told me that too. he also told me that you couldn't change the equation to get different coverage patterns.......red flag syndrome.....

in Christ, because of God's grace,

roy

[bodcaw boy]

does the wave curve because of friction on the wall? well right at the wall, the velocity should be zero so it would dictate that wave would bend. kinda of like looking at flowing water in pipe; if you look at the model, one of the assumptions is that at the wall the velocity is zero. have i ever seen it? no.

Roy,

I know that I am responding to quite an old post, but I've only just read it for the first time today when the thread was updated with a new response.

Please understand that I'm an engineer, but my specialty is signal processing not acoustics, so my understanding of acoustic waveguide theory is not as complete as I'd like. That said, don't acoustic waves propagate according to Huygen's Principle? If so, then the curvature of the wave front can intuitively be explained by differences in path length. If the portion of the sound wave adjacent to the wall propagates along the wall, while the portion of the sound wave in the "center" of the horn propagates straight down the center of the horn, and both propagate at the speed of sound, then the wave front has to curve.

Maybe the easiest way to visualize this is to think of a point source in a flat baffle as a degenerate horn with instantaneous 90° flare. The wavefront will be hemispherical, not planar.

BTW; the path length "L" (along the wall) of a circular Tractrix horn is easily computed from the Tractrix defining equation as: L=a*ln(r2/r1), where a is the mouth radius and r1, r2 are radii between which you want to know the path length (this corresponds to the nomenclature used by Bruce Edgar in his 1981 Speaker Builder article). So the path length (along the wall) of an entire Tractrix horn is L=a*ln(a/r1), where r1in this case is the throat radius. From the defining equation for the Tractrix it can easily be shown that the path length is much longer than the horn itself, meaning that the portion of the sound wave that propagated down the "center" of the horn exits the mouth long before the portion that hugged the wall even reaches the mouth. Hence, the "bubble" model of horn propagation.

Greg

as to how the wave expands, we are only guessing and the equations have assumptions. that is why at this point, we can only look at the input and evaluate the output. my bubble thingy is just an observation on helping my puny mind understand the expansion of acoustic waves. my son was blowing bubbles one day and it dawned on me what assumptions i had made erroneously. also understand, as an tinker, i have only begun to try to understand acoustics. acoustic pressures and how we tear up the bubble really intrigue me. doc post's paper helped me understand why on one point tractrix was working. the assumption in the wave equation of a plane wave traveling down the horn led many to the assumption of max power transfer occuring in an exponentially expanding area. change that assumption to spherical, and now max power transfer occurs with a tractrix expanding area. no, not perfect is right. that is why i say a modified tractrix equation.

as a tinker, i am mainly interested in getting somewhere; not in the details of how i got there.

in Christ, because of God's grace,

roy

[Edgar]

i guess i better throw away all those good measuring, good sounding bass horns i did in the tractrix form.......

dr edgar told me that too.  he also told me that you couldn't change the equation to get different coverage patterns.......red flag syndrome.....

At work just the other day we were discussing the fact that our measured data didn't agree very well with our simulated data. Somebody recommended taking more measurements. I recommended developing better simulations.

Greg