Tractrix vs. exponential

[Endo]

1. In simple terms, how exactly does a tractrix differ from an exponential horn in its design?

 

2. Also, what might be expected if the exponential horn from an earlier Heritage series driver were switched out with an equivalent Traxtrix version? From a listener's point of view, are all frequencies equally affected? (I'm particularly interested in hearing from anyone who has experienced this).

 

3. Anything else of interest?

Edited March 22, 2017 by Endo

[babadono]

from our very own fellow forum members:

 

[babadono]

from wiki tiki tavi:

https://en.wikipedia.org/wiki/Horn_loudspeaker

[babadono]

2 hours ago, Endo said:

1. In simple terms, how exactly does a tractrix differ from an exponential horn in its design?

Sorry but how does one explain acoustical horn geometries and mathematics in "simple terms"?

 

2 hours ago, Endo said:

2. Also, what might be expected if the exponential horn from an earlier Heritage series driver were switched out with an equivalent Traxtrix version? From a listener's point of view, are all frequencies equally affected? (I'm particularly interested in hearing from anyone who has experienced this).

It will sound mo' better This is just my ears and auditory cortex's opinion.

 

 Welcome to the forum Endo

[CECAA850]

[CECAA850]

21 minutes ago, babadono said:

Sorry but how does one explain acoustical horn geometries and mathematics in "simple terms"?

With pictures!

[derrickdj1]

Exp. horn will have more high frequency beaming.  The older Heritage speaker where commonly three way design since exp. horn work better when designed to emphasize either a high or low frequency.  Tractrix horns have less beaming and are designed based on the speakers low frequency extension.  These are more suited to the two way design.

 

That is my simplified understanding.

[djk]

The Hughes (Peavey) is a conical, with a Quadratic throat (and sound quite good, odd 1.6" throat though).

[Chris A]

8 hours ago, Endo said:

2. Also, what might be expected if the exponential horn from an earlier Heritage series driver were switched out with an equivalent Tractrix version? From a listener's point of view, are all frequencies equally affected? (I'm particularly interested in hearing from anyone who has experienced this).

Note that the tractrix horns provided by Klipsch are not "tractrix horns" per se.  They are modified tractrix horns.  That means that they're designed for a very special set of properties.  Note that none of the above profiles that were posted are the same as the Klipsch modified tractrix profile.

 

All frequencies handled by the horn/driver of the two different horn designs (exponential vs. modified tractrix) are not affected by the same amount.  Generally, the lower the frequency, the more audible will be the difference, although the modified tractrix horns also have a wider coverage angle at high frequencies, which will also affect the overall sound.  There is math involved and a little physics, but specifically the modified tractrix horn will sound more neutral and have a more consistent coverage angle vs. frequency.    It will sound better from a wider variety of listening azimuths and elevations than the exponential--eliminating the "head in a vise" stuff.  You can move around your room a great deal more and still hear the same timbre/soundstage.

 

The most notable differences have been the exponential midrange horns of the Klipsch Heritage series vs. the modified tractrix horns--the K-510 and the K-402, and the other modified tractrix designs on the Forte II, Chorus II, Quartet, etc.  Other Klipsch loudspeakers now use modified tractrix like the K-510 and the K-402, only typically much smaller and crossed over usually at a higher frequency.  Many of these "home theater" loudspeakers have 90x90 degree coverage angles, instead of the 90 x 60 degree coverage of the K-510 and K-402. 

 

Chris

[Chris A]

8 hours ago, Endo said:

3. Anything else of interest?

If you change only the horn in an existing Klipsch loudspeaker using an exponential midrange horn to use a modified tractrix horn, you will unbalance the frequency response of the entire loudspeaker if you do not re-equalize all the drivers/horns.  You need something like REW, and an active crossover to DIY unless you're pretty handy with redesigning passive crossovers.

[Endo]

Impressive. You guys are great... Sincere 'thank you' to all who posted. The demonstrated understanding and clarity is more than I expected (although, this is the first place I thought of as a source of true and correct info).  Thanks, again.

 

[As an aside: In my experience, complex and esoteric subjects (eg. astrophysics, cellular biology, color theory] can be explained to children in a meaningful way. The limiting factor is not so much complexity of topic as it is the understanding of the one doing the explaining. ]

[CECAA850]

14 hours ago, Chris A said:

the modified tractrix horns--the K-510

I'd love to be able to understand how Roy figured out how to form the mumps.

[richieb]

^^^^^

I've heard he takes the circumference of Bonnie Raitts cheeks in full croon, and divides by four. Don't quote me here as this is merely rumor.

[Chris A]

On 3/23/2017 at 8:05 AM, CECAA850 said:

I'd love to be able to understand how Roy figured out how to form the mumps.

Well, that one is actually at least partially understood from comments that Roy and Tom Danley have made.

 

It's well known that many horns exhibit a "waistbanding" close to their low frequency cutoff, such as that which is exaggerated in the following figure:

 

 

If you look carefully, what you're seeing is the expansion rate of the horn isn't matching what the internal acoustic waves would see in a "properly expanding horn".  Those acoustic waves are mostly spherical in shape as they propagate down the horn's length.

 

When you take a straight-sided horn and calculate the expansion rate vs. frequency, you'll see that initially it has an extremely high expansion rate but the rate of expansion slows down as you move toward the mouth of the horn.  (This is the major reason why a pyramid-shaped horn is used in multiple-entry horns - such as the Synergy horns, since the expansion rate of the horn must support the frequencies of the off-axis drivers that are injecting their acoustic energy at lower frequencies than the apex-mounted compression driver.  Danley talks about this a great deal in his first patent: US6411718)

 

When the expansion rate is too high for the supporting frequencies of a compression driver in a straight-sided horn, the acoustic wave effectively "detaches" from the wall and you get that waistbanding effect at some lower frequency.  If you provide some support in the form of bumps (or mumps) from the horn's walls at the point where that detachment occurs, the acoustic wave remains attached to the wall, and you avoid that waistbanding effect.

 

Roy talked about using modeling clay inside a K-510 horn to do a "cut and try" iterative approach to determining the correct shape, size, and placement circumferentially along the axis of the horn of those bumps.  I believe that's just what he did--and got a patent on...

 

If you also look at multiple-entry horns, the off-axis drivers are injecting their energy at the proper place in the horn, they can use the same straight-sided horn profile without mumps because the acoustic energy at those lower frequencies stay attached to the walls of the horn. 

 

Chris

[CECAA850]

Great visual and explanation Chris, thanks. 

[Dawson's Ridge]

FWIW - My Palladium P-37 speakers would qualify as modified Tractrix. I have them toed in where the midrange is pointing at the outside of each ear. From my listening chair (which is centered between the speakers - 12x12 triangle) the imaging and soundstage is very good. But if I move off axis the slightest amount I no longer have the same quality imaging and soundstage. 

[Chris A]

Try toeing them in such that the centerline of the loudspeakers cross ~1-2 feet in front of your listening position.  Make sure that no acoustically reflective objects reside between your Palladiums.  Repeat experiment.  You should have a wider sweet spot.

 

Chris

[avguytx]

It was mentioned about changing out an exponential horn with a tractrix above. I've pondered that for my Belle clones in building one that would fit in the stock size top hat if I stay 3-way.  Is shortening the tractrix horn to that low of a height going to negate the advantage of using a tractrix in the first place?

[ClaudeJ1]

On 3/22/2017 at 8:09 PM, Endo said:

Impressive. You guys are great... Sincere 'thank you' to all who posted. The demonstrated understanding and clarity is more than I expected (although, this is the first place I thought of as a source of true and correct info).  Thanks, again.

 

[As an aside: In my experience, complex and esoteric subjects (eg. astrophysics, cellular biology, color theory] can be explained to children in a meaningful way. The limiting factor is not so much complexity of topic as it is the understanding of the one doing the explaining. ]

Nothing like asking a bunch of horn guys about horns!!

 

[Chris A]

23 hours ago, avguytx said:

It was mentioned about changing out an exponential horn with a tractrix above. I've pondered that for my Belle clones in building one that would fit in the stock size top hat if I stay 3-way.  Is shortening the tractrix horn to that low of a height going to negate the advantage of using a tractrix in the first place?

Converting my center Belle to a JuBelle using a K-510 midrange horn/K-69-A compression driver,  and a Beyma CP25 tweeter increased the smoothness and the width of the soundstage significantly. 

 

That was the center loudspeaker configuration between my two Jubilees that I used before going to the K-402-MEH a year later.

 

Chris