Tractrix and Exponential Horns

[Deang]

I just lost another chromosome while reading this thread.

Now John Warren -- are you telling me you're a closet two-way adherant?

[John Warren]

deang-no, a 2 way is too much of a compromise for me.

my current *experiment* is two JBL 2123J direct radiator mid units atop each Klipschorn bass unit (four drivers total). these units are 103 db/W/m each so no issues with efficiency. these are 16 ohm drivers so wired in parallel yeilds 8 ohms with an array sensitivity of 103 db/W/m. the result to my ears is outstanding. with drivers like these around it makes no sense to buy horn loaded mids.

I'm trying numerous tweeters.

[jnorv]

What is the upper useful frequency of the 2123J's?

J Norvell

[John Warren]

JN

ruler flat from ~100Hz - 5.5kHz. I'm crossing the Klipschorn bass unit over at 400Hz and the JBLs at 4kHz (10x). Picked them up on the JBL tent sale $130 ea free shipping. list price was ~$160 in the early 90s. cloth surrounds too, no rot, will last forever.

John

[John Warren]

Mark

The 2123Js are 10" units. a vertical array pair,

wired in parallel, is good match for a single folded unit (103 dB/W/m -3dB +3dB = 103dB/W/m). 2cd order harmonic distortion is low at SPL extremes.

Mid-range realism is convincing. Piano sounds like a piano!

tweeters-

I am using a borrowed pair of ST-350s. the JBL 2404 Bi-Radial (baby cheeks) horn tweeter was what I had in mind. at 105 dB/W/m will need a bit of attenuation which can be accomplished by some drapes in the listening room. Beyma has a similar unit too that is also lower in cost.

[Chris A]

I believe I understand what an exponential horn is, but I've never seen an explanation of what a Tractrix horn purports to be. Can anyone explain "in words of one cylinder" what a Tractrix horn is and its advantages and disadvantages vs. an exponential horn? Thanks.

 

Another extremely old thread that someone was recently reading.  To simply answer the question:

 

1) the difference between a tractrix expansion horn and an exponential horn, both built for the same low cutoff frequency, is that the tractrix horn will have a mouth that is flush with the front baffle, i.e., the mouth rolls out until it smoothly joins the exit plane of the front of the speaker.

 

2) the throat of the tractrix is exactly the same as an exponential horn, i.e., there is no difference

 

3) the tractrix horn will be about 90% of the length of the exponential horn

 

4) the tractrix horn will sound more neutral, especially in smaller rooms with plenty of nearfield reflections

 

There's more...the tractrix horn expansion assumes that all the wavefronts inside the horn are spherical, while the exponential expansion assumes that all wavefronts are flat--plane waves, and exit as flat wavefronts. 

 

...I think that they should be spherical, BTW--if anyone cares...

 

Exponential horns have better low frequency response than tractrix horns--all other things being equal, but you're paying for that flat response with more distortion...of  the even harmonic kind at high SPL.

 

Look at it this way: it only took 14 years for the OP to get a simple answer to his question.

 

Chris

Edited May 18, 2016 by Chris A

[Schu]

I thought what defines a Tractrix is a curved or flared wall of the horn...

[Chris A]

Everything in above post is true.  If you want a good article that discusses the tractrix vs. exponential expansion, read Bruce Edgar's article on the subject.  It's a pretty interesting article.

 

Chris

[Chris A]

BTW: Edgar got the discussion on the German "spherical wave horn" expansion wrong--just skip that part of the article.

 

Chris

[Deang]

"Look at it this way: it only took 14 years for the OP to get a simple answer to his question."

It's not a "simple answer". It's only simple if you already understand it. It helps when there are people who can take it down a notch for the layperson. I thought the posts by Gil, Garrison, and Kerry Geist were very good. Combined - they provide a more than adequate explanation.

Since Roy keeps referring to the 402 as "modified tractrix", I found Kerry Geist's response especially interesting.

Edited May 19, 2016 by Deang

[WMcD]

It is a perennial subject.

 

The article from the Klipsch people is here.

 

https://community.klipsch.com/index.php?/topic/44607-article-re-tractrix-horn/page-3?hl= tractrix  article

 

If you go down to frame 50 you'll see that mas assembled a pdf of the article along with my annotations to some graphs from the article.

 

Please note Keist's comments above about how the horn described in the article is not a pure tractrix but that the center section was modified in the interest of maintaining directivity.  That allowed a taller mouth, the effects of which I pointed out. 

 

Roy states that his horns are modified tractrix.  It seems to me that such description only tells us what it is not rather than what it (they?) is.

 

In horn designs much of what is new can be found in the work of the ancients.

 

Don Keele's article on "What's So Sacred" figured the optimum point to match a hyperbolic horn at the throat to conical bell (the larger section).  I ddi some math to look at that and found it is the location where the rate of expansion of the two are matched.  Yet one of the ancients described about the same putting an exponential horn in a corner.

 

Keele described the K-5 as the grandfather (or like that) to constant directivity horns. With the fins removed, it seems to be more like a conical expansion even though PWK apparently modified the top and bottom walls to make it more exponential.

 

Keele in another article described optimum mouth size.  He included the diagrams by Olson which went up to ka= about 0.93 IIRC and stopped showing the results of a larger mouth.  Keele worked out that 0.93 is optimum.  I conclude that Olson must have known, but didn't tell, the rat fink.

 

These days there is a lot of thought that conical bell sections have fewer internal reflections per Geddes.  He seems to use a short exponential section at the throat.  So we're back to the ancients.

 

The bottom line IMHO is that adherence to any pure theoretical design has problems which can be (and is) tinkered with.

 

WMcD

[Chris A]

On 5/18/2016 at 5:56 PM, Deang said:

Since Roy keeps referring to the 402 as "modified tractrix", I found Kerry Geist's response especially interesting.

 

Look at figure 9 of Bruce Edgar's tractrix article to see how Roy's modified tractrix horns are constructed.  They're really "modified tractrix" sections--not conical.

 

I find that most people pay too much attention to the horn length and too little attention to the mouth area when looking at horns of this type.  Edgar's article also helps you to see this in figs. 4-6. The K-402 is actually effective down to about 35 Hz due to its mouth size--in corner loading.  It's about 41 Hz for wall/floor loading, and ~125 Hz for free standing.

 

Chris

[twk123]

Now the big question is: if Tractrix horns are better than exponential, will Klipsch ever build a Heritage model with a Tractrix mid horn instead of the current exponential? That is a tough balance between being true to the heritage of PWK and the modern developments that we see in say the Reference series. I have heard many good things from the guys with the fastlane aftermarket ones.

[Deang]

The Forte II and Chorus II both utilize Tractrix mid horns - courtesy of Bruce Edgar.

Dave Harris builds rock solid products - they are built exactly the way Dr. Edgar suggests - dual layers sandwiched together to squelch resonances - which are glued and screwed together.

[WMcD]

Now the big question is: if Tractrix horns are better than exponential, will Klipsch ever build a Heritage model with a Tractrix mid horn instead of the current exponential? That is a tough balance between being true to the heritage of PWK and the modern developments that we see in say the Reference series. I have heard many good things from the guys with the fastlane aftermarket ones.

Very good question.

 

I'm under the impression that the sale of Klipsch & Associates may have contained some restrictions on just how much the K-Horn could be changed under the contract of sale. 

 

I certainly don't know if the K-400 / 401 is absolutely required.  Since I don't know anything.

 

But, it strikes me that just maybe the K-5 would be considered an original Klipsch design for the K-Horn.  It could be modified to take a two inch driver and then it would be close to a tractrix. 

 

WMcD

[Bubo]

The Forte II and Chorus II both utilize Tractrix mid horns - courtesy of Bruce Edgar.

Dave Harris builds rock solid products - they are built exactly the way Dr. Edgar suggests - dual layers sandwiched together to squelch resonances - which are glued and screwed together.

 

I don't recall listening to a Chorus 2, but listened extensively to a Forte 2, and would easily list it as the best "sleeper" I have ever heard.

 

If memory serves me correctly, it has a number of tricks inc rear radiators, tweeter flare also tractrix?

 

Interesting photo with Fortes next to Cornscalas, is the Large horn tractrix and or the tweeter?

 

Does the Belle Bass Horn design approach Tractrix dimensions?

 

As to the question does a speaker have to rabidly adhere to the original design to be "Heritage"?

 

As a former product manager I would say no, the products were sold for their performance at an obtainable price. I don't see any problem with either bringing out a Cornwall 4, or Forte 3 etc.

 

As always there are lots of engineering trade-offs in any product.

 

[richieb]

The Forte II and Chorus II both utilize Tractrix mid horns - courtesy of Bruce Edgar.

Dave Harris builds rock solid products - they are built exactly the way Dr. Edgar suggests - dual layers sandwiched together to squelch resonances - which are glued and screwed together.

I can say this Dean I bought my KHorns already modified with the full Fastlane top hat with his 280hz Elliptrac. They are smooth as butta', excellent imaging just a real pleasure to hear. I have been giving serious consideration to Jubilee clones w/402 but I am blessed with a near perfect KHorn room and after listening last night I just can't imagine the Jubes being THAT much better. Better maybe but at a cost of over double what I have in the KHorns I'm certainly not jumping the gun. These K's are really superb.

[JohnA]

O.K., What is the change in sensitivity between a Tractrix and exponential horn using the same compression driver?

[derrickdj1]

I don't know if sensitivity difference gives that much useful info.  The main difference is the expansion rate of the horn and reflections.  The tractix wins hands down.  Now, there are speaker with average and excellent execution of the design.  This may be more important in a three design than some of Klipsch 2 way.  In general, the tractix will have lower distortion so, in a 3 way design the XO points in an expo. horn are very important.

[JohnA]

It does if you are building a crossover and need to match levels.  I have specs for a tweeter on an exponential horn, but not the Tractrix I want to use.