Tractrix in 1*Pi and 2*Pi

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There are a few theories around about how to go from full 4*Pi horns. We should know that a Tractrix is designed from the mouth and back.

One is that you calculate your full horn with four of the drivers you will use. When going to 1*Pi you use one driver, divide all horndata with four except length that remains the same. Question is how to do it from 4*Pi to 2*Pi with the same drivers, should one design with two drivers going to two? This should actually leave us with a longer horn in 2*Pi than in 1*Pi!

The second is to truncate the horn that is what HR uses. This means the mouth does not longer end at 90 degrees.

The third is to go for what Voigt recommended in his 1929 patent. This is called mirroring. You just take the 4*Pi horn and slice the sides off that are against sidewall, floor or both. See picture.

Personally I know the third works(anyway i 2*Pi) like it should IRL.

Any thoughts on this?
 

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Method #4

There are a few theories around about how to go from full 4*Pi horns. We should know that a Tractrix is designed from the mouth and back.

One is that you calculate your full horn with four of the drivers you will use. When going to 1*Pi you use one driver, divide all horndata with four except length that remains the same. Question is how to do it from 4*Pi to 2*Pi with the same drivers, should one design with two drivers going to two? This should actually leave us with a longer horn in 2*Pi than in 1*Pi!

The second is to truncate the horn that is what HR uses. This means the mouth does not longer end at 90 degrees.

The third is to go for what Voigt recommended in his 1929 patent. This is called mirroring. You just take the 4*Pi horn and slice the sides off that are against sidewall, floor or both. See picture.

Personally I know the third works(anyway i 2*Pi) like it should IRL.

Any thoughts on this?

Hi R,

Issues
The principal determinants of the acoustics of a low frequency horn are its length and mouth size. If you change either you have a different horn no matter how you ‘slice and dice’ it. Furthermore, as soon as you position a horn along a room wall, floor or more, you have also changed it acoustically. Its low frequency response will be extended, irrespective of what regimen you choose to use to design it.

Method #4, al la Klipsch
The best approach would be to lower design [fc] and extend horn length to support the longer wavelengths that are now possible. The number of drivers used is related only to the magnitude of [vd] that you require. If you cannot get it by increasing [xmax] of a single driver of a given [sd], then as you increase [sd], with larger or multiple drivers, you foreshorten horn length only, while holding dimensions of the horn mouth constant. Sometimes driver [sd] is increased to mitigate packaging constraints as horn footprint is reduced by bifurcating and folding it up into a room corner. In this case driver [xmax] may be reduced.

Regards,

WHG
 
Hey WHG,

Furthermore, as soon as you position a horn along a room wall, floor or more, you have also changed it acoustically. Its low frequency response will be extended, irrespective of what regimen you choose to use to design it.

This is what we talk about. So we need to find a way to compensate(in some way reduce size) the Tx to get approximately the same characteristics as in 1*Pi. Surely it can not be optimized, but an OK approximation might be done. Question is which is the best/worst, number one or three?

The Klipsch method might no be what to be used here(but maybe my English isn´t good enough). We are only talking about variations where the same single driver is used.

And off course it is also about to minimize size of the Tx when used in 2*Pi or 1*Pi compared to a full Tx.

To clarify we are not talking of lowbass-horns.
 
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Notes:

1) A horn is a band-pass device good for about a decade of bandwidth. A low pass frequency is always at issue in its design.
2) Note that above 200 Hz. (entering the 2nd. Decade) the ear can detect where a signal is coming from and when it is delayed. Early reflections off of room boundaries at frequencies above this limit should be avoided.
3) Unlike a LF horn that utilizes room boundaries, design of a MF horn using these methods is contradicted. This fact preempts a discussion about how to do it.
4) Out of a room corner a mouth perimeter approximating a [c]/(8*[fc]) may be used. If such a horn is used above 200 Hz. disappointing results may be expected in the upper response region.
5) For the upper two decades, use horns with fully formed mouths. If you want to reduce the length of the MF horn in may be designed as a reflex (reentrant) horn without much sacrifice in performance.
Regards,
WHG
 
New method for reducing a Tractrix from 4*Pi to 1*Pi?

Let´s take it from another angle. This is a design-theory that has been presented to me in another forum:

Calculate a full, 4*Pi, midbass horn with four drivers. When going to 1*Pi you use one of the drivers, divides all horndata with four, except length that stays the same.
This way the horn-mouth will still end at 90 degrees. It will also give a shorter horn than if we initially designed it with one driver.

Wonder what we should call the horn? Maybe a Tractrix-bastard?
 
Let´s take it from another angle. This is a design-theory that has been presented to me in another forum:

Calculate a full, 4*Pi, midbass horn with four drivers. When going to 1*Pi you use one of the drivers, divides all horndata with four, except length that stays the same.
This way the horn-mouth will still end at 90 degrees. It will also give a shorter horn than if we initially designed it with one driver.

Wonder what we should call the horn? Maybe a Tractrix-bastard?

How could this be shorter if you are keeping the length the same as a full size horn? Is it because the throat would be huge for the full size horn with 4 drivers?

This would probably not be a tractrix shape any more.
 
Hey Dirk,
Thought it was obvious, even though I didn´t mentioned it in my last post, that we should compare the length to a regular tractrix designed with one driver from the start(theory three).

It fullfills one of the issues we normally associate with Tractrix as it ends at 90 degrees. If it follows the tangential flare I don´t know, but probably not.

A truncated as in HR follows the shape towards the throat end where it gets more and more as a expontential/Hypex the more we shorten it:

 
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Hey Dirk,
Thought it was obvious, even though I didn´t mentioned it in my last post, that we should compare the length to a regular tractrix designed with one driver from the start(theory three).

It fullfills one of the issues we normally associate with Tractrix as it ends at 90 degrees. If it follows the tangential flare I don´t know, but probably not.

A truncated as in HR follows the shape towards the throat end where it gets more and more as a expontential/Hypex the more we shorten it:

Hej, sorry for the confusion on my part. I just use Hornrsp and a spreadsheet I got from a website "volvotrade" I think. I don't dig into the actual math of the programs. I just assume they got it right.
 

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There is in no way necessary for a horn to be good whatever its flare. If you play around a little you will soon find your design is equal to a Hypex:).

David and I have different ideas about Tractrix design. Search Audioasylum with author "revintage" and subject "tractrix". Long old thread with amongst others Jean-Michel and David. Thats why I brought the subject up again after having seen "theory one".

Can mail you a spredsheet where one more easily can see how Tractrix is calculated. But HR is perfect when going for full Tx.
 
There is in no way necessary for a horn to be good whatever its flare. If you play around a little you will soon find your design is equal to a Hypex:).

David and I have different ideas about Tractrix design. Search Audioasylum with author "revintage" and subject "tractrix". Long old thread with amongst others Jean-Michel and David. Thats why I brought the subject up again after having seen "theory one".

Can mail you a spredsheet where one more easily can see how Tractrix is calculated. But HR is perfect when going for full Tx.

OK, I don't see how this horn is like a Hypex, but that's OK. I'm not an expert on horn theory. I tried putting this horn into different spaces in Hornresp and got a much smoother response with it in a corner. I seem to recall that the spreadsheet I used was set to 1/4 sized though.... hmmm...

As to your third theory, how much do you slice off? How close does the horn's mouth have to be to a corner, a wall or a floor to work as a 1*pi or 0.5*pi horn?

I'm certainly willing to try a different spreadsheet for designing the horn. Thanks.
 
Hey,
Noticed your driver data is wrong. With correct data it sims even better in constant directivity! But use directivity. Unfortunately it lifts a lot even at 15 degrees off-axis.

OK. Which numbers are wrong?
My datasheet from B&C shows:
Sd = 522cm^2
Mmd (mms?) = 37gm
I don't have Cms or Rms
Bl = 19.1 Tm
Le = 1.2mH
Re = 5.8 ohms

Thanks for paying attention!
 
Here's what I got by sticking this horn into a corner. The low -3dB point seems to reach down to the designed 60Hz cutoff. Maybe I make this straight horn with 90 degree included angle so that if fits into a corner.
 

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You shouldn´t follow the datasheet alltogether. Use the recommended procedure, probably shown in the Help-section.

To see the similarity between the horntypes you can use the export-function to compare flares in Excel. But thisn´t important just try to find a fine design whatever the type it is.
 
You shouldn´t follow the datasheet alltogether. Use the recommended procedure, probably shown in the Help-section.

To see the similarity between the horntypes you can use the export-function to compare flares in Excel. But thisn´t important just try to find a fine design whatever the type it is.

OK. I looked through the help section of Hornresp and could not find what you are saying about a recommended procedure. Thanks for your help!

I did not intend that this thread become a discussion about this particular horn I'm designing. Sorry about that!
 
David and I have different ideas about Tractrix design. Search Audioasylum with author "revintage" and subject "tractrix". Long old thread with amongst others Jean-Michel and David. Thats why I brought the subject up again after having seen "theory one".

Can mail you a spredsheet where one more easily can see how Tractrix is calculated. But HR is perfect when going for full Tx.

OK, I don't have time right now to search on Audioasylum. Maybe later. Thanks for the heads up.
 
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