A friend of mine has asked for some advice about making a large (3 foot square mouth) tractrix horn. He wants to make it out of four pieces of thin ply, joined edge to edge. It will then be strengthened. His problem is how to draw the curve of each edge.
I cannot get my head round how to create that curve. Any suggestions?
I cannot get my head round how to create that curve. Any suggestions?
Some horn curve profiles are shown here.
https://freespeakerplans.com/kunena/17-midrange/4504-mid-plan
https://volvotreter.de/downloads/150Hz_Midbass_Tractrix_Horn_v1.3a.pdf
https://freespeakerplans.com/kunena/17-midrange/4504-mid-plan
https://volvotreter.de/downloads/150Hz_Midbass_Tractrix_Horn_v1.3a.pdf
Use the spreadsheet calculator (by Volvotreter) for the profile linked in post 1 of Trynergy thread. That’s how I made the horn for my Trynergy.
Presenting the Trynergy - a full range tractrix synergy.
https://www.diyaudio.com/forums/multi-way/261427-trynergy-range-tractrix-synergy-10.html#post4049533
Presenting the Trynergy - a full range tractrix synergy.
https://www.diyaudio.com/forums/multi-way/261427-trynergy-range-tractrix-synergy-10.html#post4049533
Thank you for all your replies. A lot of those shown are not 4 curved sides, but 2 curved sides and 2 flat sides. The tractrix curve is easy to get and works for a circular cross section. It is realising the curve along the edges of the four pieces to create a square tractrix that I am flumoxxed by.
I'm not sure what you mean. Is this the type of horn you have in mind?
BD-Design - Front Horn Design
Yes, that BD-Design is a square tractrix horn.
I now see your problem. You want a template for the shape of each of the four pieces of plywood which, when bent, will meet along the edges to form the tractrix horn flare.
I haven't done this, but there are members out there who must have done. Help anyone?!
I now see your problem. You want a template for the shape of each of the four pieces of plywood which, when bent, will meet along the edges to form the tractrix horn flare.
I haven't done this, but there are members out there who must have done. Help anyone?!
That certainly looks like what my friend wants. The crucial line is where bd says
"The outcome is valid for a circular horn, but simply to transfer to a square model."
That I do not get. I have suggested to my friend that he tries contacting bd, to find out what he did.
The problem is if you draw the four pieces with a tractrix curve for their edges, when you join them together you do not have a tractrix expansion in the horn.
"The outcome is valid for a circular horn, but simply to transfer to a square model."
That I do not get. I have suggested to my friend that he tries contacting bd, to find out what he did.
The problem is if you draw the four pieces with a tractrix curve for their edges, when you join them together you do not have a tractrix expansion in the horn.
There are advantages to a linear expansion on two of the walls. The area expansion is still a tractrix, so you have the benefits of superb efficiency and impedance matching between the driver and the air column. On the linear expansion axis, the polar dispersion is more well controlled and directed. The tractrix curve basically expands out to 180deg. If you make all 4 walls curved, I am not sure it will give any performance benefit other than to look symmetric aesthetically.
Interesting history to this. My friend's friend has a pair of original Voigt full wave tractrix horns!! (Which have a 4 feet square mouth)
He would like a smaller version of same. The thought is that Voigt must have worked out how to do this (assuming the originals are accurate tractrixes)
He would like a smaller version of same. The thought is that Voigt must have worked out how to do this (assuming the originals are accurate tractrixes)
That is a very interesting and valid point that you make XRK in post #11. It would win it over for me.
The person asking for the horns is a Voigt (and Lowther) collector and enthusiast. I fear he might want a pure 3 foot replica. Let's hope not.
The person asking for the horns is a Voigt (and Lowther) collector and enthusiast. I fear he might want a pure 3 foot replica. Let's hope not.
If he has the horn on hand, easiest thing to do is take a larger sheet of paper and lay it into the contour of the horn petal and trace the intersection. Then take that and go to reprographics (blueprints) store and reduce to scale. Scaling tractrix works very well.
You can also take a photo of resulting 2d trace plan with low distortion camera lens from above. A 50mm or (normal perspective lens) is best. Take image and use CAD program to overlay a spline on the curve. Then you can scale arbitrarily and even check to see if 4 of them glued at intersection forms a good horn. Probably best to make two panels extra big so that two panels can join in a “T”.
The theory of extracting a curved panel 4-petal horn from a tractrix expansion is some math that could also be done. If you are handy with theory, that could also be a very good way to go.
You can also take a photo of resulting 2d trace plan with low distortion camera lens from above. A 50mm or (normal perspective lens) is best. Take image and use CAD program to overlay a spline on the curve. Then you can scale arbitrarily and even check to see if 4 of them glued at intersection forms a good horn. Probably best to make two panels extra big so that two panels can join in a “T”.
The theory of extracting a curved panel 4-petal horn from a tractrix expansion is some math that could also be done. If you are handy with theory, that could also be a very good way to go.
An aspect of the scaling is that presumably the mouth of the horn would be reduced by 3/4. Might this be a problem in that the same drive unit as the 4 foot horn would be used?(Voigt field coil, or it's derivative Lowther PMx)
I have to say that the maths is way beyond me or my friend.
I would use a smaller driver else it will sound choked upon reduction
In scale. The square vertices of the throat of the horn should not be too much smaller than the diameter of the driver.
In scale. The square vertices of the throat of the horn should not be too much smaller than the diameter of the driver.
You don't have to be handy with theory - this functionality is built into Hornresp.
Simulate a tractrix horn of the size you want
Export Horn Data
Choose "Petal Horn" option
Choose 4 in "Petals or Sides" dropdown
Happy to help. Note that I agree with the other stuff xrk was saying, notably the stuff in post 11.
Something like this
Check out my new horns!
...doesn't look that far from symmetric, but will measure a little better on-axis.
Maybe not a huge improvement overall, but I like improvements that you can get for free. Me, I'd also make the throat a little off symmetric - e.g. a 9cm high x 5 cm wide throat for a driver that has a 10cm diameter.
Dunno if you / they have already seen this link, 'tis a great visual guide.
doityourselfaudio: 140Hz Petal Horns
Thanks for all your help. I am not sure from a purist point of view that the 2 flat sides model gives a true tractrix. The tractrix expands out to 180 degrees, which cannot be realised with flat sides.
The drivers that will be used were used for the Voigt corner horn. That had a constricted throat, and for some reason this got rid of the peaks in the driver "in the raw". I have heard the Voigt Domestic Corner Horn with Lowther PM6a drivers and the shout and shriek that one associates with those drivers was wholly absent.
The drivers that will be used were used for the Voigt corner horn. That had a constricted throat, and for some reason this got rid of the peaks in the driver "in the raw". I have heard the Voigt Domestic Corner Horn with Lowther PM6a drivers and the shout and shriek that one associates with those drivers was wholly absent.