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Tractrix Horn Generator

by mechadense, published

Tractrix Horn Generator by mechadense Jan 3, 2014
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Summary

(for now keep crop factor >0.9 in customizer - for reason see below)
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This is a generator for horns with tractrix crossection.
Those are not the same as spherical wave horns. See here:
https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf
http://audioxpress.com/ax-supplementary-material/
under: Horn Theory: An Introduction, Part 1
http://www.audioxpress.com/files/2008/03/kolbrek2884.pdf
and: Horn Theory: An Introduction, Part 2
http://www.audioxpress.com/files/2008/04/kolbrek2885.pdf
Horns act as acoustic impedance matching transformators
transformating high pressure low speed to low pressure high speed sound waves or vice versa.
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Note that the sizes that are printable on common personal 3D printers are only suitable for rather high frequencies (even for whistles).
Well as it turns out low frequencies get amplified as well.
See: http://www.thingiverse.com/thing:389700
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Example horn:
cutoff frequency: 4500Hz
inlet inner diameter: 20mm
inlet outer diameter: 24mm
inlet pipe length: 5mm
horn length cropped to: 80%
cropped horn mouth diameter: 126.5mm
complete horn length: 129.9mm
tractrix segment length: 124.9mm
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known problem: customizer can't deal with this file :(
found out: crop factor above 0.9000 works

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I would like to use this, but im worried about what runthroughthejungle said.
I have checked the source code and I cant understand this lines regarding mouth radius:

//lower cutoff wavelength
lambda_c = c_sound/fc;
// horn mouth radius
rm = lambda_c1000;
//echo("Horn mouth diameter is: ",2
rm);

Shouldn't it be.......?

//lower cutoff wavelength
lambda_c = c_sound/fc;
// horn mouth radius
rm = (lambda_c1000)/(2pi);
//echo("Horn mouth diameter is: ",2*rm);

As runthroughthejungle said, i think the code is generating a mouth radius 2*pi times bigger.

Hi mechadense, i spent some time using your generator , and i like it a lot.
i observed that the horns generated were too big , and looking at the traktrix mouth radius' formula (Rm=C/2piF),where c is speed of sound ,pi is 3,14142.. , and F is cutoff frequency, i think that the frequency coded in the generator is 2*pi times bigger.
Hope this helps, thanks for your great job.

Thanks, I will look into this when I find the time.

It could also be that customizer doesnt like cylinder(r1=<>, r2=<>,h=<>), maybe try replacing with cylinder(<r1>. <r2>, <h>, [0,0,<iterated height="">])</iterated></h></r2></r1>

sorry that got busted, the message board thought i was trying to type xml

Thanks for looking into the code,

r_add=0 is just a default value - this should work - I think I've done that before.
Also that r1= r2= h= ... input value assignment markers should work.
I too suspect too many polygons as the cause or the many almost coplanar surfaces.
Playing with the eps value for "co-planarity reduction" does not help.

I could heavily change the model to make a 2D cross-section and rotate extrude it 360°
but than I would have to choose a fixed resolution (due to the lack of mutable/dynamic arrays in OpenSCAD) :S

Interestingly in customizer the inlet cutting cuboid is visible as if the
tactrix-outer-hull-main-body where not recognized at all and the cuboid where the
first object in the difference. Also the cuboid seems to not be shifted to the inlet side.

I took a look at the code. Looks like you are just stacking cylinders. It could be that there are too many polygons, it could also be that odd calling of "module tractrixhorn_shape(r_add=0)". It is possible that openscad knows how to handle that but customizer doesn't. Seems to me that nothing should be defined in the input of a module. Hope it helps.

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