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Old 24th August 2013, 10:00 PM   #1
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Default The Downward Spiral

Most of the horns I build are for the car, and in the car, we often have to cram horns into really strange dimensions.

I've done a bunch of work with various permutations of radial horns. These include:

Click the image to open in full size.
Smith horns

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Underdash HLCDs

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Paralines

While working on these various horns, I've noticed a few things that can improve the performance of all of these devices. (Since they're all radial horns at heart.)

IMHO, these are things that help:

1) Keep the height of the pathways as small as possible. As the height of the horn grows, you start to see comb filtering that repeats itself from a certain frequency and up. For instance, with a radial horn height of just 0.2" you can confine the comb filtering to the last half octave or so; but if you have a height of 0.75" you'll see comb filtering that affects the last couple octaves. (This probably has to do with the height of the horn; 0.2" is one quarter wavelength of 16,875hz, and there's probably a correlation between the height of a radial horn and it's upper frequency limit.)

2) Unfortunately, the requirement for very very short height creates a problem. It makes the horn too small at midrange frequencies.

An obvious solution would be to vary the height of the horn. But varying the height of a radial horn can be a challenge in designs like the Paraline, which is a radial horn that's been folded in half. (Note that the fold is not straight, but that's the subject of another one of my threads named 'square pegs.'
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Old 24th August 2013, 10:12 PM   #2
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I think I may have come up with an alternative to varying the height of the radial horn. I believe that you could achieve the same goal by inserting a spiral into the radial horn.

Click the image to open in full size.

By inserting a spiral at the throat, we've basically made the pathlength longer.

How much longer depends on the spiral.

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My spiral in image number one basically takes the radial radiation of a radial horn, and it 'twists' the pathway so that it's 57.07% longer than it would be normally. (pi / 4)

There are lots of other spirals that are available as well; I chose the one in image number one because it's very easy to build.

Click the image to open in full size.
Just take some PVC pipe, quarter it, and array it around your driver at increments of 90 degrees.

I'm not 100% sure, but I believe that any horn profile could be made into a spiral. Basically take the two dimensions horn profile, slice it into four segments, then rotate those around the center.

Click the image to open in full size.

Click the image to open in full size.

For instance, here's a fibonacci shell in it's 'normal' form, and also sliced and diced into a spiral.
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Old 24th August 2013, 10:39 PM   #3
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Click the image to open in full size.

Maybe my math is failing me, but I couldn't figure out a mathematically perfect way to get these into Hornresp. Or at least nothing that was easy.

Due to that, I used some shorthand:

In a spiral like the one above, the pathlength is 57.07% longer, while the area of the segments is 63.66% as large.

For instance, in a 'normal' radial horn that was 1.91cm tall (0.75") with a radius of 6.03cm driven by a 1" compression driver, the pathlength would be 5.4cm. (The distance from the exit of the compression driver to the exit of the radial horn.
But in a spiral like the one pictured above, the pathlength increases to 8.48cm. To compensate for the increase in pathlength, I'd calculate the horn as if it's height was 1.22cm tall, instead of 1.91cm tall.

Again, this is just a bit of shorthand; in the real world you'd want to measure it with a mic. But it's a way to reflect that the volume of the horn has not changed, but the pathlength of the horn *has*.
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Old 25th August 2013, 02:51 AM   #4
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Ever think of building a Cornu Spiral horn? Now you can!

Last edited by Greebster; 25th August 2013 at 02:53 AM.
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Old 25th August 2013, 03:25 AM   #5
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Default Mega LOLs

Further down the downward spiral. No? Not a NIN fan then...
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Old 25th August 2013, 07:08 AM   #6
Zero D is offline Zero D  United Kingdom
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Good thinking

Yours appears different to the Corno. From what i can gather, your sound enters the spiral face on, not sideways ?

Ask D.McB about simming it in HR
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Old 26th August 2013, 03:08 PM   #7
badman is offline badman  United States
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I'm not quite sure I'm following the concept- are we talking about taking a sectoral throat and twisting it, or simply adding a spiral shape into the throat? I don't picture (intuitively) either working- the simple addition of a spiral shape would just be a minor disruption in the throat, and the twisted sectoral/spiral would likely be very hard on wavefront coherence- the pathlength within each "cell" widely varying.

But, you're a builder- build and test, these are just back of napkin thoughts upon seeing the premise.

Edit: Wait- just realized what you mean- single cell but curved, with the driver mounted facing (somewhat) away from the direction of the mouth- I'll be interested to see what you come up with!
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Last edited by badman; 26th August 2013 at 03:11 PM. Reason: Moment of clarity.
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Old 26th August 2013, 08:36 PM   #8
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Default Spyro Gyra

First the musical diversion
Spyro Gyra Official Site

Now for some brief notes follow: on the subject of spirals used in acoustics design.

Whirl
Whirl -- from Wolfram MathWorld

Mice
Mice Problem -- from Wolfram MathWorld

Note: If rotation is made a function on axial length as well, then the resulting vanes become helixes (and dispersive).

Daniel Ciesinger’s Cornu Sprial Horn
Audio

Clothiod (Euler’s Sprial)
Cornu Spiral -- from Wolfram MathWorld

As curvature is a function of arc length, this spiral is used in both acoustic horn and roadway design.

The profile of the Le Cléac’h horn approximates a pair of these curves.

Like the design of roadway curves, spiral segments can be used to form the boundaries of horn folds that minimize perturbation of the acoustic wave that travels through them.

Regards,

WHG

Last edited by whgeiger; 26th August 2013 at 08:48 PM.
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Old 26th August 2013, 09:09 PM   #9
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