Klipsch Bass Horn Acoustic Analysis

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Hi,

I did a search through the bass woofer design area of the site, and did not find a dedicated analysis of the K-horn. With that in mind, I tried to consider factors which could affect the acoustic performance of this corner horn.

My hope is that others who have more experience will contribute to this thread.

A Klipsch corner bass horn is analyzed for acoustic performance potential by:
  • Constructing the physical cabinet using software
  • Unfolding the acoustic sound path
  • Determining the rear cabinet trapped air volume
  • Determine the effect on acoustic performance

This shows a portion of the internal construction of the Klipschorn horn loudspeaker.
01.jpg

One quarter of the cabinet is shown in this view. This is an approximation of the average acoustic air propagation path.
02.jpg

The 3D model of the cabinet is broken into a 2D image so that the acoustic air propagation path can be determined mathematically.
03.jpg

The 2D path is then dimensioned for both area and acoustic length. Key measurement areas are identified with markers.
04.jpg

This shows the detail around the horn throat. Area dimensions are shown in green and path lengths in red.
05.jpg

Wherever possible, acoustic path lengths consider the “nominal” distance, not max or min. This is a top view of cabinet, where it folds toward the corner wall.
06.jpg

All the areas and acoustic lengths are tabulated here. The areas listed amount to ¼ of the total horn area (for sqin.) The area listed in sqcm is the total area.
07.jpg

Now the corner horn acoustic path can be unfolded with dimensions as shown below.
08.jpg

The drawing is then re-rendered without all the dimensions, which tend to obscure the drawing. One can clearly see the abrupt change in area near the horn throat. David McBean informed me that this is referred to a "rubber throat" by Klipsch.
09.jpg

The rear chamber trapped air volume is modeled based on numerous 2D dimensions around the speaker mounting plate.
10.jpg

Continued....
 
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Klipsch Bass Horn Acoustic Analysis - cont.

Another view of the rear cavity volume.
11.jpg

Finally, a third view of the rear cavity volume. The trapped air volume is 4968 cubic inches. This volume does not consider the effect of the speaker frame and magnet assembly.
12.jpg

Modeling the K-horn with a K-33 driver as shown below. I am assuming low values for Fr and Tal as shown below. Note that David McBean helped verify the K-33 parameters. Thanks David.
13.jpg

Examining the horn schematic clearly shows the “step” in the horn throat. Apparently this was done by design, by Klipsch.
14.jpg

The low end frequency response starts at about 45 Hz and then starts to drop noticably above 300 Hz.
15.jpg

Jim.
 
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One can clearly see the abrupt change in area near the horn throat. David McBean informed me that this is referred to a "rubber throat" by Klipsch.

Just to clarify - Paul Klipsch referred to the initial parabolic segment shown in red in the attachment, as a "rubber throat".

To quote PWK:

"The initial taper is such that the horn area doubles in a length of about 8 inches, corresponding to a cut-off of 100 cycles. The remainder of the horn flares at such a rate that the area doubles every 16 inches so that the nominal cutoff is 47 cycles. This results in a "rubber throat" the area of which is about 100 square inches up to 100 cycles and decreases with frequency until at 400 cycles the effective throat area is 50 square inches."
 

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Found It!

For what it is worth, my early attempt at simulating a Klipschorn nearly 50 years ago, based on information contained in Paul Klipsch's original 1941 "Low Frequency Horn of Small Dimensions" J.A.S.A. paper.

In the attached the Hornresp model, the driver parameters have been updated to K-33 specifications, but the horn and chamber dimensions remain unchanged. The first segment was originally specified as Con because I didn't have a parabolic horn model back then. It turns out that there is virtually no difference in the response anyway, even when the theoretically more correct Par expansion is used.
 

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For what it is worth, my early attempt at simulating a Klipschorn nearly 50 years ago...

Oh, oh, you don't want to give away your age too quickly. :)

...., based on information contained in Paul Klipsch's original 1941 "Low Frequency Horn of Small Dimensions" J.A.S.A. paper.

In the attached the Hornresp model, the driver parameters have been updated to K-33 specifications, but the horn and chamber dimensions remain unchanged. The first segment was originally specified as Con because I didn't have a parabolic horn model back then. It turns out that there is virtually no difference in the response anyway, even when the theoretically more correct Par expansion is used.

David, I also noticed several other things from your parameter screen shot:

  • Your measured total horn length is 148 cm and mine is 172. I did carry the length along with wall as if there was a "top-hat" on top of the bass cabinet, so that could be the difference.
  • Your final mouth opening is smaller by a proportional amount.
  • The Vrc of your model is some 37% smaller. I would bet that you have considered the effect of the K-33 driver volume reduction. I did not have one to model.
  • Fr and Tal are both zero on your model, and this would match the cut-away pictures I have seen of K-horns from various sources.

This raises a question that I have wondered about for some time now. David, did you create Hornresp to model a K-horn? Was that your first stimulus for creating the program?

Jim.
 
Not just a great work, but also another (strong) confirmation of PWK's genius engineering mind .......

thank you , both

Zen Mod, thank you for the kind words. :)

And I agree with your assessment of Mr. Klipsch. I have admired the K-horn for many years, probably more due to it's quirkiness and high efficiency than anything else. There something magical about a bass sound that emanates from inside the cabinet and comes out each side, along the walls. A true corner horn!

Jim.
 
Delgado's Notes

The attachments address design of the H.F. Horn.
WHG
 

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Hi Jim,

  • Your measured total horn length is 148 cm
  • Your final mouth opening is smaller
  • The Vrc of your model is some 37% smaller

Way back then, not having anything else to work with, I simply used the information provided by Paul Klipsch in his 1941 paper:

Throat area = 50 square inches (or 322.58 cm2)
Mouth area = 570 square inches (or 3677.41 cm2)

Rubber throat length = 13 inches (or 33.02 cm)
Main horn length = 45.5 inches (115.57 cm)

Rear chamber volume = 3600 cubic inches (or 58.99 litres)

The position of the horn mouth, which ultimately determined the horn length, is shown in the attachment.

David, did you create Hornresp to model a K-horn? Was that your first stimulus for creating the program?

Yes. I didn't know it at the time, but it seems that I may have been one of the early pioneers in using a digital computer to simulate the performance of a horn loudspeaker. Before then, it was all done using slide rules and mechanical calculators :).

Kind regards,

David
 

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Have you considered building one of these?
Also the horn/driver you put on top is more important.
See Delgado's notes attached in next message.
WHG

Hi whgeiger,

Hey, thankyou! This is a paper that was trying to get a hold of about six months ago. There was a website that allowed one to make a plea with the AES paper author and I submitted a request, but never heard anything back.

I did download a patent paper for the Jubilee, and have done a tentative acoustic analysis of that horn, and will be revisiting this topic in a future post here. Right now I am trying to focus on the older design so that I can break through some of the cobwebs in my mind right now, and to understand how to use Hornresp.

Jim.
 
....Yes. I didn't know it at the time, but it seems that I may have been one of the early pioneers in using a digital computer to simulate the performance of a horn loudspeaker. Before then, it was all done using slide rules and mechanical calculators :)....David

David, it's nice to know where your first attempts at modeling a speaker came from. I'm also glad that you have the electrical background and can meld that with mechanical to allow modeling of acoustic enclosures.

Thanks, Jim.
 
the two plots with different rear chamber volume show the effect of reactance annuling as PWK calls it. the smaller chamber has just a bit more output near 45Hz.
guess that the orginal driver is stiffer than nowadays units.

basreflex,

Your comments are insightful. I noticed the same effect in the low frequency response at cutoff. If the rear chamber volume really is close to 81 L (minus woofer magnet volume and basket), then that area is currently too large for the K-33 driver.

Jim.
 
It is more than 40 years ago that I built my first Klipsch horn. I found the original article in the university library. I had to scale it slightly smaller to fit it under the window of my campus room. it has some carpentry challenges.. I had acess to a PDP11 computer that ran fortran, so I did my first trials calculating horn impedance.. never got the bessels right , until my CPU acess ran out.
 
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