Round Tractrix

[djk]

"Have you read anything about this?"

HOM is code for internal reflections in the horn.

The lowest
reflections are from a axis-symetrical (round) horn that has the same
taper rate from inside the driver all the way to the mouth.

The
popular TAD monitors designed by Keith Holland were a double 15", 10",
and a round horn designed for the 1" TAD 2001.

'Around the Horn'
by Keith Holland was published in Speaker Builder 8/94.

http://www.audioheritage.org/vbulletin/showthread.php?t=12967

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Posted by djk (M) on November 27, 2004 at 00:23:28
In Reply
to: Re:
Soundstage depth and horns... posted by GedLee LLC on November 26, 2004
at 15:25:16:


This is mainly for Paul and eso:
Dr
Keith Holland BSc PhD did his thesis on horn loudspeakers at the
Institute of Sound and Vibration Research (ISVR), University of
Southampton.

Excerpts were published in Speaker Builder
Magazine (Reflecting on Echoes and the Cepstrum, 1996) and Liberty
Instruments offered some dedicated test equipment.

Echos were
found in many horns.

A new horn was designed to have no
echos.

It was found that any change in the taper rate of the
horn/driver combo, any inside corner, or diffration slot, produced
reflections inside the horn (echos).

The new horn was
circular and had the same taper rate as the stub inside the driver.


The new horn was based on the TAD2000 series driver and was
crossed at the point where it had the same directivity as the mid-bass
driver.

After the success of the Holland monitor, Yamaha and
Ramsa both came out with a series of products based on these ideas.


JAES:

Volume 38 Number 3 pp. 148, 149; March 1990
(Comments on "Impulse Measurement of Acoustic Impedance")


Volume 44 Number 1/2 pp. 23-36; January/February 1996 (The Sound of
Midrange Horns for Studio Monitors)

Volume 44 Number 7/8 pp.
569-580; July/August 1996 (A Model of Nonlinear Wave Propagation in
Horns)

"It is concluded that the reflections from the mouth
termination of long horns is responsible for the characteristic sound
and that for studio monitor applications, a midrange horn should have a
length not exceeding 340 mm and should be free of flare
discontinuities."

"A blind listening test is described in
which 16 loudspeakers are compared with four reference loudspeakers
under anechoic conditions. The test is concerned with the perceived
sonic similarity between midrange horn loudspeakers and direct radiators
and is intended to pinpoint the physical cause of a "characteristic
sound" attributed to many studio monitor systems equipped with
midfrequency-range horns. Comparisons are made between the listening
test results and measurements of on-axis frequency response. The results
indicate that short horns sound more similar to direct-radiating
loudspeakers than long horns."

[Al Klappenberger]

Dave,

I'm off a running.

I got the program doing a Tractrix area taper down to the throat. The next thing will be to taper the ellipse of the mouth down to a round driver.

I have been doing programing so I haven't read the latest comments yet.

Dennis,

I could easily add a conical taper section at the throat. Can you point me to any guidelines for how long to make it and to what diameter. Is it worth doing?

Al K.

[Guest David H]

Dave,

I'm off a running.

I got the program doing a Tractrix area taper down to the throat. The next thing will be to taper the ellipse of the mouth down to a round driver.

I have been doing programing so I haven't read the latest comments yet.

Dennis,

I could easily add a conical taper section at the throat. Can you point me to any guidelines for how long to make it and to what diameter. Is it worth doing?

Al K.

You have been busy. Nice

[Al Klappenberger]

Dave,

Here's guts of the program. I just need to check it over and add the variables. Right now it is fixed at 15 steps and tapers from elliptical to round in 15 linear steps.

AL K.

[Al Klappenberger]

Dave,

Here's the first practical draft of the program. Check your email.

I'll look into the HPGL interface next. This might take a bit longer!

Al K.

[cfelliot]

Just a stupid question:

Wouldn't it make sense to have the transition steps from round to ellipse be non linear so that the change in angle would be equal from step to step in both x and y?

[Al Klappenberger]

cfelliot,

I'm not sure I follow your question, but the material thickness determines the "step". I think that means the "step" must be linear. That is, number of steps = horn length / material thickness. In fact, I just modified the program so that you can input step thickness rather then how many steps if you want to.

The last sample run shows a .585 in step. It would need to be made of .50 in think stuff to be practical. That would require 11.7 steps. You would need to do 12 and shave a bit off the throat end to get it right. The internal "loop" will overrun "round" just slightly.

Is that what you mean?

Al k.

[cfelliot]

No Al.

I don't mean the step in the thickness.

I mean the step in the transition from round to the final ellipse.

[Al Klappenberger]

OH!

I think that taper could be just about anything. I did linear because it was easy to do. Can you think of any reason to change the oval to round taper rate?

Also, explain where the angle you mentioned would be.

Al K.

[cfelliot]

I'm not sure, but every round triax I've seen terminates at a 90 degree flare. The square ones on my JBLs are also that way.

You tell me, do you think it has any effect? That's why it may have been a stupid question! [8-|]

[Al Klappenberger]

cfelliot,

OOPS! I misunderstood yet again! The Tractrix expansion will force the mouth edges to be perpendicular to you. What I was saying was that the rate at which the ellipse at the mouth, as you look straight into the horn, turns into a round hole for the driver at the throat. I have it making the transition gradually, in a linear fashion, as you move down the horn from Mouth to throat. It could make that transition at any rate. I would have no idea what would sound best!

Al K.

[Guest David H]

Al, I got the program up and running, I will try some layouts in Corel hopefully tomorrow. I would like to get you a working prototype of a Midrange and tweeter for testing. What Fc would you think best suit a tweeter?

I will try and cram a 300hz elliptical in a KHorn frame with a tweeter. I have some ideas.

BTW, this program is really nice with the addition of layer thickness, takes away the guesswork.

Dave.

[Al Klappenberger]

Dave,

I think maybe 2400 Hz for the tweeter horn. I say that because the tweeter filter on the Universal network is 20 dB down at that frequency. 3700 Hz is 10 dB down. I think that would be fine too, maybe even better.

I just sent you version 1.3a of the program. It makes AutoCad files and a text file of all the segments not just the 18 or less that show to keep from scrolling off the screen.

Al k.

[Al Klappenberger]

It looks like that cutoff will make a horn that is just too small.

Here's a run of a horn with a mouth of 4 X 3 Inches. It's 1.6 Inch long and has an Fc of under 1300 Hz! It's made of 14 segments if 1/8 inch thick stuff.

Al K.

[Guest David H]

It looks like that cutoff will make a horn that is just too small.

Here's a run of a horn with a mouth of 4 X 3 Inches. It's 1.6 Inch long and has an Fc of under 1300 Hz! It's made of 14 segments if 1/8 inch thick stuff.

Al K.

Al, I will experiment with the tweeters. I suspect due to the shallow depth, I can use a lower fc and still get the HF extension needed.

Here is the sample output from the elipse horn. I hope to have a working prototype later this week for testing. This is a single layer only.

BTW, does anyone else build an elipse tracrix horn?

Dave.

[brians7]

Im in. May I request a 1in Throat, Cutoff frequence between 800hz and 1200hz, Elliptical Tractrix Flare at 90 Degrees Horizonal Coverage and 60 Degrees Vertical Coverage please. Thanks Brian

[cfelliot]

Al,

Would you be willing to give the source code to this calculator?

I'd love to look at it and do a Windows port with some graphics.

Chuck

[crd97086]

Just a basic question as I am new to upgrades. Is the round tractrix better superior to the rectangular that has been used forever, and before with many other exponential and types of horns(see wikipedia horn loaded speakers)? I am curious about how to upgrade my soon to be reburished LaScalas and I am willing to throw the tophat portion away as I have cut it off and solidified the bassbin to cut the resonance factor. Any suggestions? Much appreciated.
a

[Al Klappenberger]

I am no horn expert. As I understand it, any abrupt change in the internal flare causes reflections within the horn, Even the square corners where the flat top joins the curved sides in the Edgar type Tractrix horns a discontinuity that will cause reflections. I know from my experience at microwave frequency that any transmission line with discontinuities cause energy to reflect back to the source. If the wavelength to the discontinuity is large enough the reflected wave changes the impedance seen by the source. You might want to look up a device called a "Smith chart". It will also set up standing waves inside the line, or inside the horn in this case. The hope here is that a smooth transition from round to elliptical will minimize the reflections.

Al K.

[Guest David H]

Ok, I am on my second attempt at the Eliptic Tractrix ALK dubbed the "Eliptrac", The first attempt had a few minor flaws to correct.

I will post pics when it is complete.

Dave