Tractrix in 1*Pi and 2*Pi
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revintage
diyAudio Member

Join Date: May 2007
Tractrix in 1*Pi and 2*Pi

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?
Attached Images
 spegling.png (25.9 KB, 230 views)

Last edited by revintage; 7th August 2011 at 12:46 PM.

 7th August 2011, 04:33 PM #2 dirkwright   diyAudio Member     Join Date: May 2011 Location: Virginia The spreadsheet I use makes any size tractrix horn end with a 90 degree flare, as far as I can tell. I don't know the details of the math involved.
whgeiger
diyAudio Member

Join Date: May 2004
Location: Pensacola, Florida
Method #4

Quote:
 Originally Posted by revintage 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

revintage
diyAudio Member

Join Date: May 2007
Hey WHG,

Quote:
 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 isnīt 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.

Last edited by revintage; 7th August 2011 at 06:15 PM.

 7th August 2011, 08:56 PM #5 whgeiger   diyAudio Member   Join Date: May 2004 Location: Pensacola, Florida 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
 7th August 2011, 09:38 PM #6 revintage diyAudio Member   Join Date: May 2007 Once again, I am interested in which of the theories will work best/worse. Once again, theory three is proven to measure and sound great IRL used as midbass-horns. So actually I was curious to find out if theory one could be an alternative. Last edited by revintage; 7th August 2011 at 09:41 PM.
 8th August 2011, 05:57 AM #7 revintage diyAudio Member   Join Date: May 2007 New method for reducing a Tractrix from 4*Pi to 1*Pi? Letīs 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?
dirkwright
diyAudio Member

Join Date: May 2011
Location: Virginia
Quote:
 Originally Posted by revintage Letīs 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.

 8th August 2011, 01:07 PM #9 revintage diyAudio Member   Join Date: May 2007 Hey Dirk, Thought it was obvious, even though I didnīt 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 donīt 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: Last edited by revintage; 8th August 2011 at 01:19 PM.
dirkwright
diyAudio Member

Join Date: May 2011
Location: Virginia
Quote:
 Originally Posted by revintage Hey Dirk, Thought it was obvious, even though I didnīt 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 donīt 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.
Attached Images
 60Hz tractrix Hornresp input.JPG (54.4 KB, 149 views) 60Hz tractrix Hornresp.JPG (44.8 KB, 148 views)

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